NAME

PDL::GSL::SF - PDL interface to GSL Special Functions

DESCRIPTION

This is an interface to the Special Function package present in the GNU Scientific Library.

FUNCTIONS

gsl_sf_airy_Ai

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Ai($x);
gsl_sf_airy_Ai($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Ai; # method call
$x->gsl_sf_airy_Ai($y, $e);

Airy Function Ai(x).

Broadcasts over its inputs.

gsl_sf_airy_Ai does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Bi

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Bi($x);
gsl_sf_airy_Bi($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Bi; # method call
$x->gsl_sf_airy_Bi($y, $e);

Airy Function Bi(x).

Broadcasts over its inputs.

gsl_sf_airy_Bi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Ai_scaled

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Ai_scaled($x);
gsl_sf_airy_Ai_scaled($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Ai_scaled; # method call
$x->gsl_sf_airy_Ai_scaled($y, $e);

Scaled Airy Function Ai(x). Ai(x) for x < 0 and exp(+2/3 x^{3/2}) Ai(x) for x > 0.

Broadcasts over its inputs.

gsl_sf_airy_Ai_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Bi_scaled

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Bi_scaled($x);
gsl_sf_airy_Bi_scaled($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Bi_scaled; # method call
$x->gsl_sf_airy_Bi_scaled($y, $e);

Scaled Airy Function Bi(x). Bi(x) for x < 0 and exp(+2/3 x^{3/2}) Bi(x) for x > 0.

Broadcasts over its inputs.

gsl_sf_airy_Bi_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Ai_deriv

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Ai_deriv($x);
gsl_sf_airy_Ai_deriv($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Ai_deriv; # method call
$x->gsl_sf_airy_Ai_deriv($y, $e);

Derivative Airy Function Ai`(x).

Broadcasts over its inputs.

gsl_sf_airy_Ai_deriv does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Bi_deriv

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Bi_deriv($x);
gsl_sf_airy_Bi_deriv($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Bi_deriv; # method call
$x->gsl_sf_airy_Bi_deriv($y, $e);

Derivative Airy Function Bi`(x).

Broadcasts over its inputs.

gsl_sf_airy_Bi_deriv does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Ai_deriv_scaled

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Ai_deriv_scaled($x);
gsl_sf_airy_Ai_deriv_scaled($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Ai_deriv_scaled; # method call
$x->gsl_sf_airy_Ai_deriv_scaled($y, $e);

Derivative Scaled Airy Function Ai(x). Ai`(x) for x < 0 and exp(+2/3 x^{3/2}) Ai`(x) for x > 0.

Broadcasts over its inputs.

gsl_sf_airy_Ai_deriv_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_airy_Bi_deriv_scaled

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_airy_Bi_deriv_scaled($x);
gsl_sf_airy_Bi_deriv_scaled($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_airy_Bi_deriv_scaled; # method call
$x->gsl_sf_airy_Bi_deriv_scaled($y, $e);

Derivative Scaled Airy Function Bi(x). Bi`(x) for x < 0 and exp(+2/3 x^{3/2}) Bi`(x) for x > 0.

Broadcasts over its inputs.

gsl_sf_airy_Bi_deriv_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Jn

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_Jn($x, $n);
gsl_sf_bessel_Jn($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Jn($n); # method call
$x->gsl_sf_bessel_Jn($y, $e, $n);

Regular Bessel Function J_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_Jn does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Jn_array

Signature: (double x(); double [o]y(num); int s; IV n=>num)
Types: (double)

$y = gsl_sf_bessel_Jn_array($x, $s, $n);
gsl_sf_bessel_Jn_array($x, $y, $s, $n);  # all arguments given
$y = $x->gsl_sf_bessel_Jn_array($s, $n); # method call
$x->gsl_sf_bessel_Jn_array($y, $s, $n);

Array of Regular Bessel Functions J_{s}(x) to J_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_Jn_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Yn

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_Yn($x, $n);
gsl_sf_bessel_Yn($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Yn($n); # method call
$x->gsl_sf_bessel_Yn($y, $e, $n);

IrRegular Bessel Function Y_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_Yn does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Yn_array

Signature: (double x(); double [o]y(num); int s; IV n=>num)
Types: (double)

$y = gsl_sf_bessel_Yn_array($x, $s, $n);
gsl_sf_bessel_Yn_array($x, $y, $s, $n);  # all arguments given
$y = $x->gsl_sf_bessel_Yn_array($s, $n); # method call
$x->gsl_sf_bessel_Yn_array($y, $s, $n);

Array of Regular Bessel Functions Y_{s}(x) to Y_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_Yn_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_In

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_In($x, $n);
gsl_sf_bessel_In($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_In($n); # method call
$x->gsl_sf_bessel_In($y, $e, $n);

Regular Modified Bessel Function I_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_In does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_I_array

Signature: (double x(); double [o]y(num); int s; IV n=>num)
Types: (double)

$y = gsl_sf_bessel_I_array($x, $s, $n);
gsl_sf_bessel_I_array($x, $y, $s, $n);  # all arguments given
$y = $x->gsl_sf_bessel_I_array($s, $n); # method call
$x->gsl_sf_bessel_I_array($y, $s, $n);

Array of Regular Modified Bessel Functions I_{s}(x) to I_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_I_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_In_scaled

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_In_scaled($x, $n);
gsl_sf_bessel_In_scaled($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_In_scaled($n); # method call
$x->gsl_sf_bessel_In_scaled($y, $e, $n);

Scaled Regular Modified Bessel Function exp(-|x|) I_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_In_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_In_scaled_array

Signature: (double x(); double [o]y(num); int s; IV n=>num)
Types: (double)

$y = gsl_sf_bessel_In_scaled_array($x, $s, $n);
gsl_sf_bessel_In_scaled_array($x, $y, $s, $n);  # all arguments given
$y = $x->gsl_sf_bessel_In_scaled_array($s, $n); # method call
$x->gsl_sf_bessel_In_scaled_array($y, $s, $n);

Array of Scaled Regular Modified Bessel Functions exp(-|x|) I_{s}(x) to exp(-|x|) I_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_In_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Kn

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_Kn($x, $n);
gsl_sf_bessel_Kn($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Kn($n); # method call
$x->gsl_sf_bessel_Kn($y, $e, $n);

IrRegular Modified Bessel Function K_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_Kn does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_K_array

Signature: (double x(); double [o]y(num); int s; IV n=>num)
Types: (double)

$y = gsl_sf_bessel_K_array($x, $s, $n);
gsl_sf_bessel_K_array($x, $y, $s, $n);  # all arguments given
$y = $x->gsl_sf_bessel_K_array($s, $n); # method call
$x->gsl_sf_bessel_K_array($y, $s, $n);

Array of IrRegular Modified Bessel Functions K_{s}(x) to K_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_K_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Kn_scaled

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_Kn_scaled($x, $n);
gsl_sf_bessel_Kn_scaled($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Kn_scaled($n); # method call
$x->gsl_sf_bessel_Kn_scaled($y, $e, $n);

Scaled IrRegular Modified Bessel Function exp(-|x|) K_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_Kn_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Kn_scaled_array

Signature: (double x(); double [o]y(num); int s; IV n=>num)
Types: (double)

$y = gsl_sf_bessel_Kn_scaled_array($x, $s, $n);
gsl_sf_bessel_Kn_scaled_array($x, $y, $s, $n);  # all arguments given
$y = $x->gsl_sf_bessel_Kn_scaled_array($s, $n); # method call
$x->gsl_sf_bessel_Kn_scaled_array($y, $s, $n);

Array of Scaled IrRegular Modified Bessel Functions exp(-|x|) K_{s}(x) to exp(-|x|) K_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_Kn_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_jl

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_jl($x, $n);
gsl_sf_bessel_jl($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_jl($n); # method call
$x->gsl_sf_bessel_jl($y, $e, $n);

Regular Sphericl Bessel Function J_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_jl does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_jl_array

Signature: (double x(); double [o]y(num); int n=>num)
Types: (double)

$y = gsl_sf_bessel_jl_array($x, $n);
gsl_sf_bessel_jl_array($x, $y, $n);  # all arguments given
$y = $x->gsl_sf_bessel_jl_array($n); # method call
$x->gsl_sf_bessel_jl_array($y, $n);

Array of Spherical Regular Bessel Functions J_{0}(x) to J_{n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_jl_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_yl

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_yl($x, $n);
gsl_sf_bessel_yl($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_yl($n); # method call
$x->gsl_sf_bessel_yl($y, $e, $n);

IrRegular Spherical Bessel Function y_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_yl does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_yl_array

Signature: (double x(); double [o]y(num); int n=>num)
Types: (double)

$y = gsl_sf_bessel_yl_array($x, $n);
gsl_sf_bessel_yl_array($x, $y, $n);  # all arguments given
$y = $x->gsl_sf_bessel_yl_array($n); # method call
$x->gsl_sf_bessel_yl_array($y, $n);

Array of Regular Spherical Bessel Functions y_{0}(x) to y_{n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_yl_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_il_scaled

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_il_scaled($x, $n);
gsl_sf_bessel_il_scaled($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_il_scaled($n); # method call
$x->gsl_sf_bessel_il_scaled($y, $e, $n);

Scaled Regular Modified Spherical Bessel Function exp(-|x|) i_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_il_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_il_scaled_array

Signature: (double x(); double [o]y(num); int n=>num)
Types: (double)

$y = gsl_sf_bessel_il_scaled_array($x, $n);
gsl_sf_bessel_il_scaled_array($x, $y, $n);  # all arguments given
$y = $x->gsl_sf_bessel_il_scaled_array($n); # method call
$x->gsl_sf_bessel_il_scaled_array($y, $n);

Array of Scaled Regular Modified Spherical Bessel Functions exp(-|x|) i_{0}(x) to exp(-|x|) i_{n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_il_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_kl_scaled

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_bessel_kl_scaled($x, $n);
gsl_sf_bessel_kl_scaled($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_kl_scaled($n); # method call
$x->gsl_sf_bessel_kl_scaled($y, $e, $n);

Scaled IrRegular Modified Spherical Bessel Function exp(-|x|) k_n(x).

Broadcasts over its inputs.

gsl_sf_bessel_kl_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_kl_scaled_array

Signature: (double x(); double [o]y(num); int n=>num)
Types: (double)

$y = gsl_sf_bessel_kl_scaled_array($x, $n);
gsl_sf_bessel_kl_scaled_array($x, $y, $n);  # all arguments given
$y = $x->gsl_sf_bessel_kl_scaled_array($n); # method call
$x->gsl_sf_bessel_kl_scaled_array($y, $n);

Array of Scaled IrRegular Modified Spherical Bessel Functions exp(-|x|) k_{s}(x) to exp(-|x|) k_{s+n-1}(x).

Broadcasts over its inputs.

gsl_sf_bessel_kl_scaled_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Jnu

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_Jnu($x, $n);
gsl_sf_bessel_Jnu($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Jnu($n); # method call
$x->gsl_sf_bessel_Jnu($y, $e, $n);

Regular Cylindrical Bessel Function J_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_Jnu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Ynu

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_Ynu($x, $n);
gsl_sf_bessel_Ynu($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Ynu($n); # method call
$x->gsl_sf_bessel_Ynu($y, $e, $n);

IrRegular Cylindrical Bessel Function J_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_Ynu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Inu_scaled

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_Inu_scaled($x, $n);
gsl_sf_bessel_Inu_scaled($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Inu_scaled($n); # method call
$x->gsl_sf_bessel_Inu_scaled($y, $e, $n);

Scaled Modified Cylindrical Bessel Function exp(-|x|) I_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_Inu_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Inu

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_Inu($x, $n);
gsl_sf_bessel_Inu($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Inu($n); # method call
$x->gsl_sf_bessel_Inu($y, $e, $n);

Modified Cylindrical Bessel Function I_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_Inu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Knu_scaled

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_Knu_scaled($x, $n);
gsl_sf_bessel_Knu_scaled($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Knu_scaled($n); # method call
$x->gsl_sf_bessel_Knu_scaled($y, $e, $n);

Scaled Modified Cylindrical Bessel Function exp(-|x|) K_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_Knu_scaled does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_Knu

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_Knu($x, $n);
gsl_sf_bessel_Knu($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_Knu($n); # method call
$x->gsl_sf_bessel_Knu($y, $e, $n);

Modified Cylindrical Bessel Function K_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_Knu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_bessel_lnKnu

Signature: (double x(); double [o]y(); double [o]e(); double n)
Types: (double)

($y, $e) = gsl_sf_bessel_lnKnu($x, $n);
gsl_sf_bessel_lnKnu($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_bessel_lnKnu($n); # method call
$x->gsl_sf_bessel_lnKnu($y, $e, $n);

Logarithm of Modified Cylindrical Bessel Function K_nu(x).

Broadcasts over its inputs.

gsl_sf_bessel_lnKnu does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_clausen

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_clausen($x);
gsl_sf_clausen($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_clausen; # method call
$x->gsl_sf_clausen($y, $e);

Clausen Integral. Cl_2(x) := Integrate[-Log[2 Sin[t/2]], {t,0,x}]

Broadcasts over its inputs.

gsl_sf_clausen does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hydrogenicR

Signature: (double x(); double [o]y(); double [o]e(); int n; int l; double z)
Types: (double)

($y, $e) = gsl_sf_hydrogenicR($x, $n, $l, $z);
gsl_sf_hydrogenicR($x, $y, $e, $n, $l, $z);    # all arguments given
($y, $e) = $x->gsl_sf_hydrogenicR($n, $l, $z); # method call
$x->gsl_sf_hydrogenicR($y, $e, $n, $l, $z);

Normalized Hydrogenic bound states. Radial dipendence.

Broadcasts over its inputs.

gsl_sf_hydrogenicR does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_coulomb_wave_FGp_array

Signature: (double x(); double [o]fc(n); double [o]fcp(n); double [o]gc(n); double [o]gcp(n); int [o]ovfw(); double [o]fe(n); double [o]ge(n); double lam_min; IV kmax=>n; double eta)
Types: (double)

($fc, $fcp, $gc, $gcp, $ovfw, $fe, $ge) = gsl_sf_coulomb_wave_FGp_array($x, $lam_min, $kmax, $eta);
gsl_sf_coulomb_wave_FGp_array($x, $fc, $fcp, $gc, $gcp, $ovfw, $fe, $ge, $lam_min, $kmax, $eta);    # all arguments given
($fc, $fcp, $gc, $gcp, $ovfw, $fe, $ge) = $x->gsl_sf_coulomb_wave_FGp_array($lam_min, $kmax, $eta); # method call
$x->gsl_sf_coulomb_wave_FGp_array($fc, $fcp, $gc, $gcp, $ovfw, $fe, $ge, $lam_min, $kmax, $eta);

Coulomb wave functions F_{lam_F}(eta,x), G_{lam_G}(eta,x) and their derivatives; lam_G := lam_F - k_lam_G. if ovfw is signaled then F_L(eta,x)  =  fc[k_L] * exp(fe) and similar. 

Broadcasts over its inputs.

gsl_sf_coulomb_wave_FGp_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_coulomb_wave_sphF_array

Signature: (double x(); double [o]fc(n); int [o]ovfw(); double [o]fe(n); double lam_min; IV kmax=>n; double eta)
Types: (double)

($fc, $ovfw, $fe) = gsl_sf_coulomb_wave_sphF_array($x, $lam_min, $kmax, $eta);
gsl_sf_coulomb_wave_sphF_array($x, $fc, $ovfw, $fe, $lam_min, $kmax, $eta);    # all arguments given
($fc, $ovfw, $fe) = $x->gsl_sf_coulomb_wave_sphF_array($lam_min, $kmax, $eta); # method call
$x->gsl_sf_coulomb_wave_sphF_array($fc, $ovfw, $fe, $lam_min, $kmax, $eta);

Coulomb wave function divided by the argument, F(xi, eta)/xi. This is the function which reduces to spherical Bessel functions in the limit eta->0. 

Broadcasts over its inputs.

gsl_sf_coulomb_wave_sphF_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_coulomb_CL_e

Signature: (double L(); double eta();  double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_coulomb_CL_e($L, $eta);
gsl_sf_coulomb_CL_e($L, $eta, $y, $e);    # all arguments given
($y, $e) = $L->gsl_sf_coulomb_CL_e($eta); # method call
$L->gsl_sf_coulomb_CL_e($eta, $y, $e);

Coulomb wave function normalization constant. [Abramowitz+Stegun 14.1.8, 14.1.9].

Broadcasts over its inputs.

gsl_sf_coulomb_CL_e does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_coupling_3j

Signature: (ja(); jb(); jc(); ma(); mb(); mc(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_coupling_3j($ja, $jb, $jc, $ma, $mb, $mc);
gsl_sf_coupling_3j($ja, $jb, $jc, $ma, $mb, $mc, $y, $e);    # all arguments given
($y, $e) = $ja->gsl_sf_coupling_3j($jb, $jc, $ma, $mb, $mc); # method call
$ja->gsl_sf_coupling_3j($jb, $jc, $ma, $mb, $mc, $y, $e);

3j Symbols: (ja jb jc) over (ma mb mc).

Broadcasts over its inputs.

gsl_sf_coupling_3j does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_coupling_6j

Signature: (ja(); jb(); jc(); jd(); je(); jf(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_coupling_6j($ja, $jb, $jc, $jd, $je, $jf);
gsl_sf_coupling_6j($ja, $jb, $jc, $jd, $je, $jf, $y, $e);    # all arguments given
($y, $e) = $ja->gsl_sf_coupling_6j($jb, $jc, $jd, $je, $jf); # method call
$ja->gsl_sf_coupling_6j($jb, $jc, $jd, $je, $jf, $y, $e);

6j Symbols: (ja jb jc) over (jd je jf).

Broadcasts over its inputs.

gsl_sf_coupling_6j does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_coupling_9j

Signature: (ja(); jb(); jc(); jd(); je(); jf(); jg(); jh(); ji(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_coupling_9j($ja, $jb, $jc, $jd, $je, $jf, $jg, $jh, $ji);
gsl_sf_coupling_9j($ja, $jb, $jc, $jd, $je, $jf, $jg, $jh, $ji, $y, $e);    # all arguments given
($y, $e) = $ja->gsl_sf_coupling_9j($jb, $jc, $jd, $je, $jf, $jg, $jh, $ji); # method call
$ja->gsl_sf_coupling_9j($jb, $jc, $jd, $je, $jf, $jg, $jh, $ji, $y, $e);

9j Symbols: (ja jb jc) over (jd je jf) over (jg jh ji).

Broadcasts over its inputs.

gsl_sf_coupling_9j does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_dawson

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_dawson($x);
gsl_sf_dawson($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_dawson; # method call
$x->gsl_sf_dawson($y, $e);

Dawsons integral: Exp[-x^2] Integral[ Exp[t^2], {t,0,x}]

Broadcasts over its inputs.

gsl_sf_dawson does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_debye_1

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_debye_1($x);
gsl_sf_debye_1($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_debye_1; # method call
$x->gsl_sf_debye_1($y, $e);

D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]

Broadcasts over its inputs.

gsl_sf_debye_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_debye_2

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_debye_2($x);
gsl_sf_debye_2($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_debye_2; # method call
$x->gsl_sf_debye_2($y, $e);

D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]

Broadcasts over its inputs.

gsl_sf_debye_2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_debye_3

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_debye_3($x);
gsl_sf_debye_3($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_debye_3; # method call
$x->gsl_sf_debye_3($y, $e);

D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]

Broadcasts over its inputs.

gsl_sf_debye_3 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_debye_4

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_debye_4($x);
gsl_sf_debye_4($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_debye_4; # method call
$x->gsl_sf_debye_4($y, $e);

D_n(x) := n/x^n Integrate[t^n/(e^t - 1), {t,0,x}]

Broadcasts over its inputs.

gsl_sf_debye_4 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_dilog

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_dilog($x);
gsl_sf_dilog($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_dilog; # method call
$x->gsl_sf_dilog($y, $e);

/* Real part of DiLogarithm(x), for real argument. In Lewins notation, this is Li_2(x). Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ]

Broadcasts over its inputs.

gsl_sf_dilog does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_complex_dilog

Signature: (double r(); double t(); double [o]re(); double [o]im(); double [o]ere(); double [o]eim())
Types: (double)

($re, $im, $ere, $eim) = gsl_sf_complex_dilog($r, $t);
gsl_sf_complex_dilog($r, $t, $re, $im, $ere, $eim);    # all arguments given
($re, $im, $ere, $eim) = $r->gsl_sf_complex_dilog($t); # method call
$r->gsl_sf_complex_dilog($t, $re, $im, $ere, $eim);

DiLogarithm(z), for complex argument z = r Exp[i theta].

Broadcasts over its inputs.

gsl_sf_complex_dilog does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_multiply

Signature: (double x(); double xx(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_multiply($x, $xx);
gsl_sf_multiply($x, $xx, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_multiply($xx); # method call
$x->gsl_sf_multiply($xx, $y, $e);

Multiplication.

Broadcasts over its inputs.

gsl_sf_multiply does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_multiply_err

Signature: (double x(); double xe(); double xx(); double xxe(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_multiply_err($x, $xe, $xx, $xxe);
gsl_sf_multiply_err($x, $xe, $xx, $xxe, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_multiply_err($xe, $xx, $xxe); # method call
$x->gsl_sf_multiply_err($xe, $xx, $xxe, $y, $e);

Multiplication with associated errors.

Broadcasts over its inputs.

gsl_sf_multiply_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_Kcomp

Signature: (double k(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_Kcomp($k);
gsl_sf_ellint_Kcomp($k, $y, $e);    # all arguments given
($y, $e) = $k->gsl_sf_ellint_Kcomp; # method call
$k->gsl_sf_ellint_Kcomp($y, $e);

Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}].

Broadcasts over its inputs.

gsl_sf_ellint_Kcomp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_Ecomp

Signature: (double k(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_Ecomp($k);
gsl_sf_ellint_Ecomp($k, $y, $e);    # all arguments given
($y, $e) = $k->gsl_sf_ellint_Ecomp; # method call
$k->gsl_sf_ellint_Ecomp($y, $e);

Legendre form of complete elliptic integrals E(k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, Pi/2}]

Broadcasts over its inputs.

gsl_sf_ellint_Ecomp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_F

Signature: (double phi(); double k(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_F($phi, $k);
gsl_sf_ellint_F($phi, $k, $y, $e);    # all arguments given
($y, $e) = $phi->gsl_sf_ellint_F($k); # method call
$phi->gsl_sf_ellint_F($k, $y, $e);

Legendre form of incomplete elliptic integrals F(phi,k) = Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Broadcasts over its inputs.

gsl_sf_ellint_F does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_E

Signature: (double phi(); double k(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_E($phi, $k);
gsl_sf_ellint_E($phi, $k, $y, $e);    # all arguments given
($y, $e) = $phi->gsl_sf_ellint_E($k); # method call
$phi->gsl_sf_ellint_E($k, $y, $e);

Legendre form of incomplete elliptic integrals E(phi,k) = Integral[ Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Broadcasts over its inputs.

gsl_sf_ellint_E does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_P

Signature: (double phi(); double k(); double n();
             double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_P($phi, $k, $n);
gsl_sf_ellint_P($phi, $k, $n, $y, $e);    # all arguments given
($y, $e) = $phi->gsl_sf_ellint_P($k, $n); # method call
$phi->gsl_sf_ellint_P($k, $n, $y, $e);

Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]

Broadcasts over its inputs.

gsl_sf_ellint_P does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_D

Signature: (double phi(); double k();
             double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_D($phi, $k);
gsl_sf_ellint_D($phi, $k, $y, $e);    # all arguments given
($y, $e) = $phi->gsl_sf_ellint_D($k); # method call
$phi->gsl_sf_ellint_D($k, $y, $e);

Legendre form of incomplete elliptic integrals D(phi,k)

Broadcasts over its inputs.

gsl_sf_ellint_D does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_RC

Signature: (double x(); double yy(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_RC($x, $yy);
gsl_sf_ellint_RC($x, $yy, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_ellint_RC($yy); # method call
$x->gsl_sf_ellint_RC($yy, $y, $e);

Carlsons symmetric basis of functions RC(x,y) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}

Broadcasts over its inputs.

gsl_sf_ellint_RC does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_RD

Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_RD($x, $yy, $z);
gsl_sf_ellint_RD($x, $yy, $z, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_ellint_RD($yy, $z); # method call
$x->gsl_sf_ellint_RD($yy, $z, $y, $e);

Carlsons symmetric basis of functions RD(x,y,z) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]

Broadcasts over its inputs.

gsl_sf_ellint_RD does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_RF

Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_RF($x, $yy, $z);
gsl_sf_ellint_RF($x, $yy, $z, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_ellint_RF($yy, $z); # method call
$x->gsl_sf_ellint_RF($yy, $z, $y, $e);

Carlsons symmetric basis of functions RF(x,y,z) = 1/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]

Broadcasts over its inputs.

gsl_sf_ellint_RF does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_ellint_RJ

Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_ellint_RJ($x, $yy, $z, $p);
gsl_sf_ellint_RJ($x, $yy, $z, $p, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_ellint_RJ($yy, $z, $p); # method call
$x->gsl_sf_ellint_RJ($yy, $z, $p, $y, $e);

Carlsons symmetric basis of functions RJ(x,y,z,p) = 3/2 Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]

Broadcasts over its inputs.

gsl_sf_ellint_RJ does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_elljac

Signature: (double u(); double m(); double [o]sn(); double [o]cn(); double [o]dn())
Types: (double)

($sn, $cn, $dn) = gsl_sf_elljac($u, $m);
gsl_sf_elljac($u, $m, $sn, $cn, $dn);    # all arguments given
($sn, $cn, $dn) = $u->gsl_sf_elljac($m); # method call
$u->gsl_sf_elljac($m, $sn, $cn, $dn);

Jacobian elliptic functions sn, dn, cn by descending Landen transformations

Broadcasts over its inputs.

gsl_sf_elljac does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_erfc

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_erfc($x);
gsl_sf_erfc($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_erfc; # method call
$x->gsl_sf_erfc($y, $e);

Complementary Error Function erfc(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,x,Infinity}]

Broadcasts over its inputs.

gsl_sf_erfc does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_log_erfc

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_log_erfc($x);
gsl_sf_log_erfc($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_log_erfc; # method call
$x->gsl_sf_log_erfc($y, $e);

Log Complementary Error Function

Broadcasts over its inputs.

gsl_sf_log_erfc does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_erf

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_erf($x);
gsl_sf_erf($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_erf; # method call
$x->gsl_sf_erf($y, $e);

Error Function erf(x) := 2/Sqrt[Pi] Integrate[Exp[-t^2], {t,0,x}]

Broadcasts over its inputs.

gsl_sf_erf does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_erf_Z

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_erf_Z($x);
gsl_sf_erf_Z($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_erf_Z; # method call
$x->gsl_sf_erf_Z($y, $e);

Z(x) : Abramowitz+Stegun 26.2.1

Broadcasts over its inputs.

gsl_sf_erf_Z does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_erf_Q

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_erf_Q($x);
gsl_sf_erf_Q($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_erf_Q; # method call
$x->gsl_sf_erf_Q($y, $e);

Q(x) : Abramowitz+Stegun 26.2.1

Broadcasts over its inputs.

gsl_sf_erf_Q does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_exp

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_exp($x);
gsl_sf_exp($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_exp; # method call
$x->gsl_sf_exp($y, $e);

Exponential

Broadcasts over its inputs.

gsl_sf_exp does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_exprel_n

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_exprel_n($x, $n);
gsl_sf_exprel_n($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_exprel_n($n); # method call
$x->gsl_sf_exprel_n($y, $e, $n);

N-relative Exponential. exprel_N(x) = N!/x^N (exp(x) - Sum[x^k/k!, {k,0,N-1}]) = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... = 1F1(1,1+N,x)

Broadcasts over its inputs.

gsl_sf_exprel_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_exp_err

Signature: (double x(); double dx(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_exp_err($x, $dx);
gsl_sf_exp_err($x, $dx, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_exp_err($dx); # method call
$x->gsl_sf_exp_err($dx, $y, $e);

Exponential of a quantity with given error.

Broadcasts over its inputs.

gsl_sf_exp_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_expint_E1

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_expint_E1($x);
gsl_sf_expint_E1($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_expint_E1; # method call
$x->gsl_sf_expint_E1($y, $e);

E_1(x) := Re[ Integrate[ Exp[-xt]/t, {t,1,Infinity}] ]

Broadcasts over its inputs.

gsl_sf_expint_E1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_expint_E2

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_expint_E2($x);
gsl_sf_expint_E2($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_expint_E2; # method call
$x->gsl_sf_expint_E2($y, $e);

E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infity}] ]

Broadcasts over its inputs.

gsl_sf_expint_E2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_expint_Ei

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_expint_Ei($x);
gsl_sf_expint_Ei($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_expint_Ei; # method call
$x->gsl_sf_expint_Ei($y, $e);

Ei(x) := PV Integrate[ Exp[-t]/t, {t,-x,Infinity}]

Broadcasts over its inputs.

gsl_sf_expint_Ei does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_Shi

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_Shi($x);
gsl_sf_Shi($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_Shi; # method call
$x->gsl_sf_Shi($y, $e);

Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}]

Broadcasts over its inputs.

gsl_sf_Shi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_Chi

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_Chi($x);
gsl_sf_Chi($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_Chi; # method call
$x->gsl_sf_Chi($y, $e);

Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ]

Broadcasts over its inputs.

gsl_sf_Chi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_expint_3

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_expint_3($x);
gsl_sf_expint_3($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_expint_3; # method call
$x->gsl_sf_expint_3($y, $e);

Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}]

Broadcasts over its inputs.

gsl_sf_expint_3 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_Si

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_Si($x);
gsl_sf_Si($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_Si; # method call
$x->gsl_sf_Si($y, $e);

Si(x) := Integrate[ Sin[t]/t, {t,0,x}]

Broadcasts over its inputs.

gsl_sf_Si does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_Ci

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_Ci($x);
gsl_sf_Ci($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_Ci; # method call
$x->gsl_sf_Ci($y, $e);

Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}]

Broadcasts over its inputs.

gsl_sf_Ci does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_atanint

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_atanint($x);
gsl_sf_atanint($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_atanint; # method call
$x->gsl_sf_atanint($y, $e);

AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]

Broadcasts over its inputs.

gsl_sf_atanint does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_fermi_dirac_int

Signature: (double x(); double [o]y(); double [o]e(); int j)
Types: (double)

($y, $e) = gsl_sf_fermi_dirac_int($x, $j);
gsl_sf_fermi_dirac_int($x, $y, $e, $j);    # all arguments given
($y, $e) = $x->gsl_sf_fermi_dirac_int($j); # method call
$x->gsl_sf_fermi_dirac_int($y, $e, $j);

Complete integral F_j(x) for integer j

Broadcasts over its inputs.

gsl_sf_fermi_dirac_int does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_fermi_dirac_mhalf

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_fermi_dirac_mhalf($x);
gsl_sf_fermi_dirac_mhalf($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_fermi_dirac_mhalf; # method call
$x->gsl_sf_fermi_dirac_mhalf($y, $e);

Complete integral F_{-1/2}(x)

Broadcasts over its inputs.

gsl_sf_fermi_dirac_mhalf does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_fermi_dirac_half

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_fermi_dirac_half($x);
gsl_sf_fermi_dirac_half($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_fermi_dirac_half; # method call
$x->gsl_sf_fermi_dirac_half($y, $e);

Complete integral F_{1/2}(x)

Broadcasts over its inputs.

gsl_sf_fermi_dirac_half does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_fermi_dirac_3half

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_fermi_dirac_3half($x);
gsl_sf_fermi_dirac_3half($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_fermi_dirac_3half; # method call
$x->gsl_sf_fermi_dirac_3half($y, $e);

Complete integral F_{3/2}(x)

Broadcasts over its inputs.

gsl_sf_fermi_dirac_3half does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_fermi_dirac_inc_0

Signature: (double x(); double [o]y(); double [o]e(); double b)
Types: (double)

($y, $e) = gsl_sf_fermi_dirac_inc_0($x, $b);
gsl_sf_fermi_dirac_inc_0($x, $y, $e, $b);    # all arguments given
($y, $e) = $x->gsl_sf_fermi_dirac_inc_0($b); # method call
$x->gsl_sf_fermi_dirac_inc_0($y, $e, $b);

Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)

Broadcasts over its inputs.

gsl_sf_fermi_dirac_inc_0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lngamma

Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
Types: (double)

($y, $s, $e) = gsl_sf_lngamma($x);
gsl_sf_lngamma($x, $y, $s, $e);    # all arguments given
($y, $s, $e) = $x->gsl_sf_lngamma; # method call
$x->gsl_sf_lngamma($y, $s, $e);

Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0. So Gamma[x] = sgn * Exp[result_lg].

Broadcasts over its inputs.

gsl_sf_lngamma does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gamma

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_gamma($x);
gsl_sf_gamma($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_gamma; # method call
$x->gsl_sf_gamma($y, $e);

Gamma(x), x not a negative integer

Broadcasts over its inputs.

gsl_sf_gamma does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gammastar

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_gammastar($x);
gsl_sf_gammastar($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_gammastar; # method call
$x->gsl_sf_gammastar($y, $e);

Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf

Broadcasts over its inputs.

gsl_sf_gammastar does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gammainv

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_gammainv($x);
gsl_sf_gammainv($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_gammainv; # method call
$x->gsl_sf_gammainv($y, $e);

1/Gamma(x)

Broadcasts over its inputs.

gsl_sf_gammainv does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lngamma_complex

Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Types: (double)

($x, $y, $xe, $ye) = gsl_sf_lngamma_complex($zr, $zi);
gsl_sf_lngamma_complex($zr, $zi, $x, $y, $xe, $ye);    # all arguments given
($x, $y, $xe, $ye) = $zr->gsl_sf_lngamma_complex($zi); # method call
$zr->gsl_sf_lngamma_complex($zi, $x, $y, $xe, $ye);

Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z)) in (-Pi, Pi]

Broadcasts over its inputs.

gsl_sf_lngamma_complex does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_taylorcoeff

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_taylorcoeff($x, $n);
gsl_sf_taylorcoeff($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_taylorcoeff($n); # method call
$x->gsl_sf_taylorcoeff($y, $e, $n);

x^n / n!

Broadcasts over its inputs.

gsl_sf_taylorcoeff does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_fact

Signature: (x(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_fact($x);
gsl_sf_fact($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_fact; # method call
$x->gsl_sf_fact($y, $e);

n!

Broadcasts over its inputs.

gsl_sf_fact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_doublefact

Signature: (x(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_doublefact($x);
gsl_sf_doublefact($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_doublefact; # method call
$x->gsl_sf_doublefact($y, $e);

n!! = n(n-2)(n-4)

Broadcasts over its inputs.

gsl_sf_doublefact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lnfact

Signature: (x(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_lnfact($x);
gsl_sf_lnfact($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_lnfact; # method call
$x->gsl_sf_lnfact($y, $e);

ln n!

Broadcasts over its inputs.

gsl_sf_lnfact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lndoublefact

Signature: (x(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_lndoublefact($x);
gsl_sf_lndoublefact($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_lndoublefact; # method call
$x->gsl_sf_lndoublefact($y, $e);

ln n!!

Broadcasts over its inputs.

gsl_sf_lndoublefact does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lnchoose

Signature: (n(); m(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_lnchoose($n, $m);
gsl_sf_lnchoose($n, $m, $y, $e);    # all arguments given
($y, $e) = $n->gsl_sf_lnchoose($m); # method call
$n->gsl_sf_lnchoose($m, $y, $e);

log(n choose m)

Broadcasts over its inputs.

gsl_sf_lnchoose does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_choose

Signature: (n(); m(); double [o]y(); double [o]e())
Types: (long)

($y, $e) = gsl_sf_choose($n, $m);
gsl_sf_choose($n, $m, $y, $e);    # all arguments given
($y, $e) = $n->gsl_sf_choose($m); # method call
$n->gsl_sf_choose($m, $y, $e);

n choose m

Broadcasts over its inputs.

gsl_sf_choose does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lnpoch

Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
Types: (double)

($y, $s, $e) = gsl_sf_lnpoch($x, $a);
gsl_sf_lnpoch($x, $y, $s, $e, $a);    # all arguments given
($y, $s, $e) = $x->gsl_sf_lnpoch($a); # method call
$x->gsl_sf_lnpoch($y, $s, $e, $a);

Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn = sgn( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]

Broadcasts over its inputs.

gsl_sf_lnpoch does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_poch

Signature: (double x(); double [o]y(); double [o]e(); double a)
Types: (double)

($y, $e) = gsl_sf_poch($x, $a);
gsl_sf_poch($x, $y, $e, $a);    # all arguments given
($y, $e) = $x->gsl_sf_poch($a); # method call
$x->gsl_sf_poch($y, $e, $a);

Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]

Broadcasts over its inputs.

gsl_sf_poch does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_pochrel

Signature: (double x(); double [o]y(); double [o]e(); double a)
Types: (double)

($y, $e) = gsl_sf_pochrel($x, $a);
gsl_sf_pochrel($x, $y, $e, $a);    # all arguments given
($y, $e) = $x->gsl_sf_pochrel($a); # method call
$x->gsl_sf_pochrel($y, $e, $a);

Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]

Broadcasts over its inputs.

gsl_sf_pochrel does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gamma_inc_Q

Signature: (double x(); double [o]y(); double [o]e(); double a)
Types: (double)

($y, $e) = gsl_sf_gamma_inc_Q($x, $a);
gsl_sf_gamma_inc_Q($x, $y, $e, $a);    # all arguments given
($y, $e) = $x->gsl_sf_gamma_inc_Q($a); # method call
$x->gsl_sf_gamma_inc_Q($y, $e, $a);

Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]

Broadcasts over its inputs.

gsl_sf_gamma_inc_Q does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gamma_inc_P

Signature: (double x(); double [o]y(); double [o]e(); double a)
Types: (double)

($y, $e) = gsl_sf_gamma_inc_P($x, $a);
gsl_sf_gamma_inc_P($x, $y, $e, $a);    # all arguments given
($y, $e) = $x->gsl_sf_gamma_inc_P($a); # method call
$x->gsl_sf_gamma_inc_P($y, $e, $a);

Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]

Broadcasts over its inputs.

gsl_sf_gamma_inc_P does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lnbeta

Signature: (double a(); double b(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_lnbeta($a, $b);
gsl_sf_lnbeta($a, $b, $y, $e);    # all arguments given
($y, $e) = $a->gsl_sf_lnbeta($b); # method call
$a->gsl_sf_lnbeta($b, $y, $e);

Logarithm of Beta Function Log[B(a,b)]

Broadcasts over its inputs.

gsl_sf_lnbeta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_beta

Signature: (double a(); double b();double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_beta($a, $b);
gsl_sf_beta($a, $b, $y, $e);    # all arguments given
($y, $e) = $a->gsl_sf_beta($b); # method call
$a->gsl_sf_beta($b, $y, $e);

Beta Function B(a,b)

Broadcasts over its inputs.

gsl_sf_beta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gegenpoly_n

Signature: (double x(); double [o]y(); double [o]e(); int n; double lambda)
Types: (double)

($y, $e) = gsl_sf_gegenpoly_n($x, $n, $lambda);
gsl_sf_gegenpoly_n($x, $y, $e, $n, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_gegenpoly_n($n, $lambda); # method call
$x->gsl_sf_gegenpoly_n($y, $e, $n, $lambda);

Evaluate Gegenbauer polynomials.

Broadcasts over its inputs.

gsl_sf_gegenpoly_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_gegenpoly_array

Signature: (double x(); double [o]y(num); int n=>num; double lambda)
Types: (double)

$y = gsl_sf_gegenpoly_array($x, $n, $lambda);
gsl_sf_gegenpoly_array($x, $y, $n, $lambda);  # all arguments given
$y = $x->gsl_sf_gegenpoly_array($n, $lambda); # method call
$x->gsl_sf_gegenpoly_array($y, $n, $lambda);

Calculate array of Gegenbauer polynomials from 0 to n-1.

Broadcasts over its inputs.

gsl_sf_gegenpoly_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_0F1

Signature: (double x(); double [o]y(); double [o]e(); double c)
Types: (double)

($y, $e) = gsl_sf_hyperg_0F1($x, $c);
gsl_sf_hyperg_0F1($x, $y, $e, $c);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_0F1($c); # method call
$x->gsl_sf_hyperg_0F1($y, $e, $c);

/* Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x])

Broadcasts over its inputs.

gsl_sf_hyperg_0F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_1F1

Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
Types: (double)

($y, $e) = gsl_sf_hyperg_1F1($x, $a, $b);
gsl_sf_hyperg_1F1($x, $y, $e, $a, $b);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_1F1($a, $b); # method call
$x->gsl_sf_hyperg_1F1($y, $e, $a, $b);

Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x)

Broadcasts over its inputs.

gsl_sf_hyperg_1F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_U

Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
Types: (double)

($y, $e) = gsl_sf_hyperg_U($x, $a, $b);
gsl_sf_hyperg_U($x, $y, $e, $a, $b);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_U($a, $b); # method call
$x->gsl_sf_hyperg_U($y, $e, $a, $b);

Confluent hypergeometric function for integer parameters. U(a,b,x)

Broadcasts over its inputs.

gsl_sf_hyperg_U does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_2F1

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Types: (double)

($y, $e) = gsl_sf_hyperg_2F1($x, $a, $b, $c);
gsl_sf_hyperg_2F1($x, $y, $e, $a, $b, $c);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_2F1($a, $b, $c); # method call
$x->gsl_sf_hyperg_2F1($y, $e, $a, $b, $c);

Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x]

Broadcasts over its inputs.

gsl_sf_hyperg_2F1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_2F1_conj

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Types: (double)

($y, $e) = gsl_sf_hyperg_2F1_conj($x, $a, $b, $c);
gsl_sf_hyperg_2F1_conj($x, $y, $e, $a, $b, $c);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_2F1_conj($a, $b, $c); # method call
$x->gsl_sf_hyperg_2F1_conj($y, $e, $a, $b, $c);

Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]

Broadcasts over its inputs.

gsl_sf_hyperg_2F1_conj does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_2F1_renorm

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Types: (double)

($y, $e) = gsl_sf_hyperg_2F1_renorm($x, $a, $b, $c);
gsl_sf_hyperg_2F1_renorm($x, $y, $e, $a, $b, $c);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_2F1_renorm($a, $b, $c); # method call
$x->gsl_sf_hyperg_2F1_renorm($y, $e, $a, $b, $c);

Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]

Broadcasts over its inputs.

gsl_sf_hyperg_2F1_renorm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_2F1_conj_renorm

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Types: (double)

($y, $e) = gsl_sf_hyperg_2F1_conj_renorm($x, $a, $b, $c);
gsl_sf_hyperg_2F1_conj_renorm($x, $y, $e, $a, $b, $c);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_2F1_conj_renorm($a, $b, $c); # method call
$x->gsl_sf_hyperg_2F1_conj_renorm($y, $e, $a, $b, $c);

Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]

Broadcasts over its inputs.

gsl_sf_hyperg_2F1_conj_renorm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hyperg_2F0

Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
Types: (double)

($y, $e) = gsl_sf_hyperg_2F0($x, $a, $b);
gsl_sf_hyperg_2F0($x, $y, $e, $a, $b);    # all arguments given
($y, $e) = $x->gsl_sf_hyperg_2F0($a, $b); # method call
$x->gsl_sf_hyperg_2F0($y, $e, $a, $b);

Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x)

Broadcasts over its inputs.

gsl_sf_hyperg_2F0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_laguerre_n

Signature: (double x(); double [o]y(); double [o]e(); int n; double a)
Types: (double)

($y, $e) = gsl_sf_laguerre_n($x, $n, $a);
gsl_sf_laguerre_n($x, $y, $e, $n, $a);    # all arguments given
($y, $e) = $x->gsl_sf_laguerre_n($n, $a); # method call
$x->gsl_sf_laguerre_n($y, $e, $n, $a);

Evaluate generalized Laguerre polynomials.

Broadcasts over its inputs.

gsl_sf_laguerre_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_Pl

Signature: (double x(); double [o]y(); double [o]e(); int l)
Types: (double)

($y, $e) = gsl_sf_legendre_Pl($x, $l);
gsl_sf_legendre_Pl($x, $y, $e, $l);    # all arguments given
($y, $e) = $x->gsl_sf_legendre_Pl($l); # method call
$x->gsl_sf_legendre_Pl($y, $e, $l);

P_l(x)

Broadcasts over its inputs.

gsl_sf_legendre_Pl does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_Pl_array

Signature: (double x(); double [o]y(num); int l=>num)
Types: (double)

$y = gsl_sf_legendre_Pl_array($x, $l);
gsl_sf_legendre_Pl_array($x, $y, $l);  # all arguments given
$y = $x->gsl_sf_legendre_Pl_array($l); # method call
$x->gsl_sf_legendre_Pl_array($y, $l);

P_l(x) from 0 to n-1.

Broadcasts over its inputs.

gsl_sf_legendre_Pl_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_Ql

Signature: (double x(); double [o]y(); double [o]e(); int l)
Types: (double)

($y, $e) = gsl_sf_legendre_Ql($x, $l);
gsl_sf_legendre_Ql($x, $y, $e, $l);    # all arguments given
($y, $e) = $x->gsl_sf_legendre_Ql($l); # method call
$x->gsl_sf_legendre_Ql($y, $e, $l);

Q_l(x)

Broadcasts over its inputs.

gsl_sf_legendre_Ql does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_Plm

Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
Types: (double)

($y, $e) = gsl_sf_legendre_Plm($x, $l, $m);
gsl_sf_legendre_Plm($x, $y, $e, $l, $m);    # all arguments given
($y, $e) = $x->gsl_sf_legendre_Plm($l, $m); # method call
$x->gsl_sf_legendre_Plm($y, $e, $l, $m);

P_lm(x)

Broadcasts over its inputs.

gsl_sf_legendre_Plm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_array

Signature: (double x(); double [o]y(n=CALC($COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1)); double [t]work(wn=CALC(gsl_sf_legendre_array_n($COMP(lmax)))); char norm;  int lmax; int csphase)
Types: (double)

Calculate all normalized associated Legendre polynomials.

$Plm = gsl_sf_legendre_array($x,'P',4,-1);

The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l on the range abs(x)<=1.

The parameter norm should be:

'S' for Schmidt semi-normalized associated Legendre polynomials S_l^m(x),

'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or

'N' for fully normalized associated Legendre polynomials N_l^m(x).

'P' (or any other) for unnormalized associated Legendre polynomials P_l^m(x),

lmax is the maximum degree l. csphase should be (-1) to INCLUDE the Condon-Shortley phase factor (-1)^m, or (+1) to EXCLUDE it.

See "gsl_sf_legendre_array_index" to get the value of l and m in the returned vector.

Broadcasts over its inputs.

gsl_sf_legendre_array processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_array_index

Signature: (int [o]l(n=CALC($COMP(lmax)*($COMP(lmax)+1)/2+$COMP(lmax)+1)); int [o]m(n); int lmax)
Types: (sbyte byte short ushort long ulong indx ulonglong longlong
  float double ldouble)

Calculate the relation between gsl_sf_legendre_arrays index and l and m values.

Note that this function is called differently than the corresponding GSL function, to make it more useful for PDL: here you just input the maximum l (lmax) that was used in gsl_sf_legendre_array and it calculates all l and m values.

Broadcasts over its inputs.

gsl_sf_legendre_array_index does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_sphPlm

Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
Types: (double)

($y, $e) = gsl_sf_legendre_sphPlm($x, $l, $m);
gsl_sf_legendre_sphPlm($x, $y, $e, $l, $m);    # all arguments given
($y, $e) = $x->gsl_sf_legendre_sphPlm($l, $m); # method call
$x->gsl_sf_legendre_sphPlm($y, $e, $l, $m);

P_lm(x), normalized properly for use in spherical harmonics

Broadcasts over its inputs.

gsl_sf_legendre_sphPlm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_conicalP_half

Signature: (double x(); double [o]y(); double [o]e(); double lambda)
Types: (double)

($y, $e) = gsl_sf_conicalP_half($x, $lambda);
gsl_sf_conicalP_half($x, $y, $e, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_conicalP_half($lambda); # method call
$x->gsl_sf_conicalP_half($y, $e, $lambda);

Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)

Broadcasts over its inputs.

gsl_sf_conicalP_half does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_conicalP_mhalf

Signature: (double x(); double [o]y(); double [o]e(); double lambda)
Types: (double)

($y, $e) = gsl_sf_conicalP_mhalf($x, $lambda);
gsl_sf_conicalP_mhalf($x, $y, $e, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_conicalP_mhalf($lambda); # method call
$x->gsl_sf_conicalP_mhalf($y, $e, $lambda);

Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)

Broadcasts over its inputs.

gsl_sf_conicalP_mhalf does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_conicalP_0

Signature: (double x(); double [o]y(); double [o]e(); double lambda)
Types: (double)

($y, $e) = gsl_sf_conicalP_0($x, $lambda);
gsl_sf_conicalP_0($x, $y, $e, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_conicalP_0($lambda); # method call
$x->gsl_sf_conicalP_0($y, $e, $lambda);

Conical Function P^{0}_{-1/2 + I lambda}(x)

Broadcasts over its inputs.

gsl_sf_conicalP_0 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_conicalP_1

Signature: (double x(); double [o]y(); double [o]e(); double lambda)
Types: (double)

($y, $e) = gsl_sf_conicalP_1($x, $lambda);
gsl_sf_conicalP_1($x, $y, $e, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_conicalP_1($lambda); # method call
$x->gsl_sf_conicalP_1($y, $e, $lambda);

Conical Function P^{1}_{-1/2 + I lambda}(x)

Broadcasts over its inputs.

gsl_sf_conicalP_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_conicalP_sph_reg

Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)
Types: (double)

($y, $e) = gsl_sf_conicalP_sph_reg($x, $l, $lambda);
gsl_sf_conicalP_sph_reg($x, $y, $e, $l, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_conicalP_sph_reg($l, $lambda); # method call
$x->gsl_sf_conicalP_sph_reg($y, $e, $l, $lambda);

Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)

Broadcasts over its inputs.

gsl_sf_conicalP_sph_reg does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_conicalP_cyl_reg_e

Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)
Types: (double)

($y, $e) = gsl_sf_conicalP_cyl_reg_e($x, $m, $lambda);
gsl_sf_conicalP_cyl_reg_e($x, $y, $e, $m, $lambda);    # all arguments given
($y, $e) = $x->gsl_sf_conicalP_cyl_reg_e($m, $lambda); # method call
$x->gsl_sf_conicalP_cyl_reg_e($y, $e, $m, $lambda);

Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)

Broadcasts over its inputs.

gsl_sf_conicalP_cyl_reg_e does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_H3d

Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)
Types: (double)

($y, $e) = gsl_sf_legendre_H3d($l, $lambda, $eta);
gsl_sf_legendre_H3d($y, $e, $l, $lambda, $eta);    # all arguments given
($y, $e) = $l->gsl_sf_legendre_H3d($lambda, $eta); # method call
$y->gsl_sf_legendre_H3d($e, $l, $lambda, $eta);

lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

Broadcasts over its inputs.

gsl_sf_legendre_H3d does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_legendre_H3d_array

Signature: (double [o]y(num); int l=>num; double lambda; double eta)
Types: (double)

$y = gsl_sf_legendre_H3d_array($l, $lambda, $eta);
gsl_sf_legendre_H3d_array($y, $l, $lambda, $eta);  # all arguments given
$y = $l->gsl_sf_legendre_H3d_array($lambda, $eta); # method call
$y->gsl_sf_legendre_H3d_array($l, $lambda, $eta);

Array of H3d(ell), for l from 0 to n-1.

Broadcasts over its inputs.

gsl_sf_legendre_H3d_array does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_log

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_log($x);
gsl_sf_log($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_log; # method call
$x->gsl_sf_log($y, $e);

Provide a logarithm function with GSL semantics.

Broadcasts over its inputs.

gsl_sf_log does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_complex_log

Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Types: (double)

($x, $y, $xe, $ye) = gsl_sf_complex_log($zr, $zi);
gsl_sf_complex_log($zr, $zi, $x, $y, $xe, $ye);    # all arguments given
($x, $y, $xe, $ye) = $zr->gsl_sf_complex_log($zi); # method call
$zr->gsl_sf_complex_log($zi, $x, $y, $xe, $ye);

Complex Logarithm exp(lnr + I theta) = zr + I zi Returns argument in [-pi,pi].

Broadcasts over its inputs.

gsl_sf_complex_log does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_poly_eval

Signature: (double x(); double c(m); double [o]y())
Types: (double)

$y = gsl_poly_eval($x, $c);
gsl_poly_eval($x, $c, $y);  # all arguments given
$y = $x->gsl_poly_eval($c); # method call
$x->gsl_poly_eval($c, $y);

c[0] + c[1] x + c[2] x^2 + ... + c[m-1] x^(m-1)

Broadcasts over its inputs.

gsl_poly_eval does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_pow_int

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_pow_int($x, $n);
gsl_sf_pow_int($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_pow_int($n); # method call
$x->gsl_sf_pow_int($y, $e, $n);

Calculate x^n.

Broadcasts over its inputs.

gsl_sf_pow_int does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_psi

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_psi($x);
gsl_sf_psi($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_psi; # method call
$x->gsl_sf_psi($y, $e);

Di-Gamma Function psi(x).

Broadcasts over its inputs.

gsl_sf_psi does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_psi_1piy

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_psi_1piy($x);
gsl_sf_psi_1piy($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_psi_1piy; # method call
$x->gsl_sf_psi_1piy($y, $e);

Di-Gamma Function Re[psi(1 + I y)]

Broadcasts over its inputs.

gsl_sf_psi_1piy does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_psi_n

Signature: (double x(); double [o]y(); double [o]e(); int n)
Types: (double)

($y, $e) = gsl_sf_psi_n($x, $n);
gsl_sf_psi_n($x, $y, $e, $n);    # all arguments given
($y, $e) = $x->gsl_sf_psi_n($n); # method call
$x->gsl_sf_psi_n($y, $e, $n);

Poly-Gamma Function psi^(n)(x)

Broadcasts over its inputs.

gsl_sf_psi_n does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_synchrotron_1

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_synchrotron_1($x);
gsl_sf_synchrotron_1($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_synchrotron_1; # method call
$x->gsl_sf_synchrotron_1($y, $e);

First synchrotron function: synchrotron_1(x) = x Integral[ K_{5/3}(t), {t, x, Infinity}]

Broadcasts over its inputs.

gsl_sf_synchrotron_1 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_synchrotron_2

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_synchrotron_2($x);
gsl_sf_synchrotron_2($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_synchrotron_2; # method call
$x->gsl_sf_synchrotron_2($y, $e);

Second synchroton function: synchrotron_2(x) = x * K_{2/3}(x)

Broadcasts over its inputs.

gsl_sf_synchrotron_2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_transport_2

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_transport_2($x);
gsl_sf_transport_2($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_transport_2; # method call
$x->gsl_sf_transport_2($y, $e);

J(2,x)

Broadcasts over its inputs.

gsl_sf_transport_2 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_transport_3

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_transport_3($x);
gsl_sf_transport_3($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_transport_3; # method call
$x->gsl_sf_transport_3($y, $e);

J(3,x)

Broadcasts over its inputs.

gsl_sf_transport_3 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_transport_4

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_transport_4($x);
gsl_sf_transport_4($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_transport_4; # method call
$x->gsl_sf_transport_4($y, $e);

J(4,x)

Broadcasts over its inputs.

gsl_sf_transport_4 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_transport_5

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_transport_5($x);
gsl_sf_transport_5($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_transport_5; # method call
$x->gsl_sf_transport_5($y, $e);

J(5,x)

Broadcasts over its inputs.

gsl_sf_transport_5 does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_sin

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_sin($x);
gsl_sf_sin($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_sin; # method call
$x->gsl_sf_sin($y, $e);

Sin(x) with GSL semantics.

Broadcasts over its inputs.

gsl_sf_sin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_cos

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_cos($x);
gsl_sf_cos($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_cos; # method call
$x->gsl_sf_cos($y, $e);

Cos(x) with GSL semantics.

Broadcasts over its inputs.

gsl_sf_cos does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hypot

Signature: (double x(); double xx(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_hypot($x, $xx);
gsl_sf_hypot($x, $xx, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_hypot($xx); # method call
$x->gsl_sf_hypot($xx, $y, $e);

Hypot(x,xx) with GSL semantics.

Broadcasts over its inputs.

gsl_sf_hypot does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_complex_sin

Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Types: (double)

($x, $y, $xe, $ye) = gsl_sf_complex_sin($zr, $zi);
gsl_sf_complex_sin($zr, $zi, $x, $y, $xe, $ye);    # all arguments given
($x, $y, $xe, $ye) = $zr->gsl_sf_complex_sin($zi); # method call
$zr->gsl_sf_complex_sin($zi, $x, $y, $xe, $ye);

Sin(z) for complex z

Broadcasts over its inputs.

gsl_sf_complex_sin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_complex_cos

Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Types: (double)

($x, $y, $xe, $ye) = gsl_sf_complex_cos($zr, $zi);
gsl_sf_complex_cos($zr, $zi, $x, $y, $xe, $ye);    # all arguments given
($x, $y, $xe, $ye) = $zr->gsl_sf_complex_cos($zi); # method call
$zr->gsl_sf_complex_cos($zi, $x, $y, $xe, $ye);

Cos(z) for complex z

Broadcasts over its inputs.

gsl_sf_complex_cos does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_complex_logsin

Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Types: (double)

($x, $y, $xe, $ye) = gsl_sf_complex_logsin($zr, $zi);
gsl_sf_complex_logsin($zr, $zi, $x, $y, $xe, $ye);    # all arguments given
($x, $y, $xe, $ye) = $zr->gsl_sf_complex_logsin($zi); # method call
$zr->gsl_sf_complex_logsin($zi, $x, $y, $xe, $ye);

Log(Sin(z)) for complex z

Broadcasts over its inputs.

gsl_sf_complex_logsin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lnsinh

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_lnsinh($x);
gsl_sf_lnsinh($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_lnsinh; # method call
$x->gsl_sf_lnsinh($y, $e);

Log(Sinh(x)) with GSL semantics.

Broadcasts over its inputs.

gsl_sf_lnsinh does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_lncosh

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_lncosh($x);
gsl_sf_lncosh($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_lncosh; # method call
$x->gsl_sf_lncosh($y, $e);

Log(Cos(x)) with GSL semantics.

Broadcasts over its inputs.

gsl_sf_lncosh does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_polar_to_rect

Signature: (double r(); double t(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Types: (double)

($x, $y, $xe, $ye) = gsl_sf_polar_to_rect($r, $t);
gsl_sf_polar_to_rect($r, $t, $x, $y, $xe, $ye);    # all arguments given
($x, $y, $xe, $ye) = $r->gsl_sf_polar_to_rect($t); # method call
$r->gsl_sf_polar_to_rect($t, $x, $y, $xe, $ye);

Convert polar to rectlinear coordinates.

Broadcasts over its inputs.

gsl_sf_polar_to_rect does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_rect_to_polar

Signature: (double x(); double y(); double [o]r(); double [o]t(); double [o]re(); double [o]te())
Types: (double)

($r, $t, $re, $te) = gsl_sf_rect_to_polar($x, $y);
gsl_sf_rect_to_polar($x, $y, $r, $t, $re, $te);    # all arguments given
($r, $t, $re, $te) = $x->gsl_sf_rect_to_polar($y); # method call
$x->gsl_sf_rect_to_polar($y, $r, $t, $re, $te);

Convert rectlinear to polar coordinates. return argument in range [-pi, pi].

Broadcasts over its inputs.

gsl_sf_rect_to_polar does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_angle_restrict_symm

Signature: (double [o]y())
Types: (double)

$y = gsl_sf_angle_restrict_symm();
gsl_sf_angle_restrict_symm($y);    # all arguments given
$y->gsl_sf_angle_restrict_symm;

Force an angle to lie in the range (-pi,pi].

Broadcasts over its inputs.

gsl_sf_angle_restrict_symm does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_angle_restrict_pos

Signature: (double [o]y())
Types: (double)

$y = gsl_sf_angle_restrict_pos();
gsl_sf_angle_restrict_pos($y);    # all arguments given
$y->gsl_sf_angle_restrict_pos;

Force an angle to lie in the range [0,2 pi).

Broadcasts over its inputs.

gsl_sf_angle_restrict_pos does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_sin_err

Signature: (double x(); double dx(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_sin_err($x, $dx);
gsl_sf_sin_err($x, $dx, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_sin_err($dx); # method call
$x->gsl_sf_sin_err($dx, $y, $e);

Sin(x) for quantity with an associated error.

Broadcasts over its inputs.

gsl_sf_sin_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_cos_err

Signature: (double x(); double dx(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_cos_err($x, $dx);
gsl_sf_cos_err($x, $dx, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_cos_err($dx); # method call
$x->gsl_sf_cos_err($dx, $y, $e);

Cos(x) for quantity with an associated error.

Broadcasts over its inputs.

gsl_sf_cos_err does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_zeta

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_zeta($x);
gsl_sf_zeta($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_zeta; # method call
$x->gsl_sf_zeta($y, $e);

Riemann Zeta Function zeta(x) = Sum[ k^(-s), {k,1,Infinity} ], s != 1.0

Broadcasts over its inputs.

gsl_sf_zeta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_hzeta

Signature: (double s(); double [o]y(); double [o]e(); double q)
Types: (double)

($y, $e) = gsl_sf_hzeta($s, $q);
gsl_sf_hzeta($s, $y, $e, $q);    # all arguments given
($y, $e) = $s->gsl_sf_hzeta($q); # method call
$s->gsl_sf_hzeta($y, $e, $q);

Hurwicz Zeta Function zeta(s,q) = Sum[ (k+q)^(-s), {k,0,Infinity} ]

Broadcasts over its inputs.

gsl_sf_hzeta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

gsl_sf_eta

Signature: (double x(); double [o]y(); double [o]e())
Types: (double)

($y, $e) = gsl_sf_eta($x);
gsl_sf_eta($x, $y, $e);    # all arguments given
($y, $e) = $x->gsl_sf_eta; # method call
$x->gsl_sf_eta($y, $e);

Eta Function eta(s) = (1-2^(1-s)) zeta(s)

Broadcasts over its inputs.

gsl_sf_eta does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

AUTHOR

This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.

The GSL SF modules were written by G. Jungman.

cpanm PDL::GSL

perl -MCPAN -e shell
install PDL::GSL