t/parse/operators.xml - metacpan.org

<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml package="latexml"?>
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<document xmlns="http://dlmf.nist.gov/LaTeXML">
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  <section inlist="toc" xml:id="S1">
    <tags>
      <tag>1</tag>
      <tag role="refnum">1</tag>
      <tag role="typerefnum">§1</tag>
    </tags>
    <title><tag close=" ">1</tag>Integration and Summation</title>
    <para xml:id="S1.p1">
      <equation xml:id="S1.Ex1">
        <Math mode="display" tex="\sum_{a=0}^{\infty}f_{a}(c^{a})" text="((sum _ (a = 0)) ^ infinity)@((f _ a)@(c ^ a))" xml:id="S1.Ex1.m1">
          <XMath>
            <XMApp>
              <XMApp scriptpos="mid">
                <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                <XMApp scriptpos="mid">
                  <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                  <XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
                  <XMApp>
                    <XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
                    <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                    <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                  </XMApp>
                </XMApp>
                <XMTok fontsize="70%" meaning="infinity" name="infty" role="ID">∞</XMTok>
              </XMApp>
              <XMDual>
                <XMApp>
                  <XMRef idref="S1.Ex1.m1.1"/>
                  <XMRef idref="S1.Ex1.m1.2"/>
                </XMApp>
                <XMApp>
                  <XMApp xml:id="S1.Ex1.m1.1">
                    <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                    <XMTok font="italic" role="FUNCTION">f</XMTok>
                    <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                  </XMApp>
                  <XMWrap>
                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                    <XMApp xml:id="S1.Ex1.m1.2">
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                      <XMTok font="italic" role="ID">c</XMTok>
                      <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                    </XMApp>
                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                  </XMWrap>
                </XMApp>
              </XMDual>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex2">
        <Math mode="display" tex="\sum_{a=0}^{\infty}\sum_{b=-a}^{a}f_{a}(c^{a})g_{b}(c^{b})" text="((sum _ (a = 0)) ^ infinity)@(((sum _ (b = - a)) ^ a)@((f _ a)@(c ^ a) * (g _ b)@(c ^ b)))" xml:id="S1.Ex2.m1">
          <XMath>
            <XMApp>
              <XMApp scriptpos="mid">
                <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                <XMApp scriptpos="mid">
                  <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                  <XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
                  <XMApp>
                    <XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
                    <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                    <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                  </XMApp>
                </XMApp>
                <XMTok fontsize="70%" meaning="infinity" name="infty" role="ID">∞</XMTok>
              </XMApp>
              <XMApp>
                <XMApp scriptpos="mid">
                  <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                  <XMApp scriptpos="mid">
                    <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                    <XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
                    <XMApp>
                      <XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
                      <XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
                      <XMApp>
                        <XMTok fontsize="70%" meaning="minus" role="ADDOP">-</XMTok>
                        <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                  <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                </XMApp>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMDual>
                    <XMApp>
                      <XMRef idref="S1.Ex2.m1.1"/>
                      <XMRef idref="S1.Ex2.m1.2"/>
                    </XMApp>
                    <XMApp>
                      <XMApp xml:id="S1.Ex2.m1.1">
                        <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                        <XMTok font="italic" role="FUNCTION">f</XMTok>
                        <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                      </XMApp>
                      <XMWrap>
                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                        <XMApp xml:id="S1.Ex2.m1.2">
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMTok font="italic" role="ID">c</XMTok>
                          <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                        </XMApp>
                        <XMTok role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMApp>
                  </XMDual>
                  <XMDual>
                    <XMApp>
                      <XMRef idref="S1.Ex2.m1.3"/>
                      <XMRef idref="S1.Ex2.m1.4"/>
                    </XMApp>
                    <XMApp>
                      <XMApp xml:id="S1.Ex2.m1.3">
                        <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                        <XMTok font="italic" role="FUNCTION">g</XMTok>
                        <XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
                      </XMApp>
                      <XMWrap>
                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                        <XMApp xml:id="S1.Ex2.m1.4">
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMTok font="italic" role="ID">c</XMTok>
                          <XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
                        </XMApp>
                        <XMTok role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMApp>
                  </XMDual>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S1.Ex3">
        <Math mode="display" tex="\sum_{a=0}^{\infty}\sum_{b=-a}^{a}\lim_{c\rightarrow 0}f_{a}(c^{a})g_{b}(c^{b})" text="((sum _ (a = 0)) ^ infinity)@(((sum _ (b = - a)) ^ a)@((limit _ (c rightarrow 0))@((f _ a)@(c ^ a) * (g _ b)@(c ^ b))))" xml:id="S1.Ex3.m1">
          <XMath>
            <XMApp>
              <XMApp scriptpos="mid">
                <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                <XMApp scriptpos="mid">
                  <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                  <XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
                  <XMApp>
                    <XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
                    <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                    <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                  </XMApp>
                </XMApp>
                <XMTok fontsize="70%" meaning="infinity" name="infty" role="ID">∞</XMTok>
              </XMApp>
              <XMApp>
                <XMApp scriptpos="mid">
                  <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                  <XMApp scriptpos="mid">
                    <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                    <XMTok mathstyle="display" meaning="sum" role="SUMOP" scriptpos="mid">∑</XMTok>
                    <XMApp>
                      <XMTok fontsize="70%" meaning="equals" role="RELOP">=</XMTok>
                      <XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
                      <XMApp>
                        <XMTok fontsize="70%" meaning="minus" role="ADDOP">-</XMTok>
                        <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                  <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                </XMApp>
                <XMApp>
                  <XMApp scriptpos="mid">
                    <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                    <XMTok meaning="limit" role="LIMITOP" scriptpos="mid">lim</XMTok>
                    <XMApp>
                      <XMTok fontsize="70%" name="rightarrow" role="ARROW">→</XMTok>
                      <XMTok font="italic" fontsize="70%" role="ID">c</XMTok>
                      <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMDual>
                      <XMApp>
                        <XMRef idref="S1.Ex3.m1.1"/>
                        <XMRef idref="S1.Ex3.m1.2"/>
                      </XMApp>
                      <XMApp>
                        <XMApp xml:id="S1.Ex3.m1.1">
                          <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                          <XMTok font="italic" role="FUNCTION">f</XMTok>
                          <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                        </XMApp>
                        <XMWrap>
                          <XMTok role="OPEN" stretchy="false">(</XMTok>
                          <XMApp xml:id="S1.Ex3.m1.2">
                            <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                            <XMTok font="italic" role="ID">c</XMTok>
                            <XMTok font="italic" fontsize="70%" role="ID">a</XMTok>
                          </XMApp>
                          <XMTok role="CLOSE" stretchy="false">)</XMTok>
                        </XMWrap>
                      </XMApp>
                    </XMDual>
                    <XMDual>
                      <XMApp>
                        <XMRef idref="S1.Ex3.m1.3"/>
                        <XMRef idref="S1.Ex3.m1.4"/>
                      </XMApp>
                      <XMApp>
                        <XMApp xml:id="S1.Ex3.m1.3">
                          <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                          <XMTok font="italic" role="FUNCTION">g</XMTok>
                          <XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
                        </XMApp>
                        <XMWrap>
                          <XMTok role="OPEN" stretchy="false">(</XMTok>
                          <XMApp xml:id="S1.Ex3.m1.4">
                            <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                            <XMTok font="italic" role="ID">c</XMTok>
                            <XMTok font="italic" fontsize="70%" role="ID">b</XMTok>
                          </XMApp>
                          <XMTok role="CLOSE" stretchy="false">)</XMTok>
                        </XMWrap>
                      </XMApp>
                    </XMDual>
                  </XMApp>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
  <section inlist="toc" xml:id="S2">
    <tags>
      <tag>2</tag>
      <tag role="refnum">2</tag>
      <tag role="typerefnum">§2</tag>
    </tags>
    <title><tag close=" ">2</tag>Operators</title>
    <para xml:id="S2.p1">
      <equation xml:id="S2.Ex4">
        <Math mode="display" tex="Da" text="D@(a)" xml:id="S2.Ex4.m1">
          <XMath>
            <XMApp>
              <XMTok font="italic" role="OPERATOR">D</XMTok>
              <XMTok font="italic" role="ID">a</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex5">
        <Math mode="display" tex="Df" text="D@(f)" xml:id="S2.Ex5.m1">
          <XMath>
            <XMApp>
              <XMTok font="italic" role="OPERATOR">D</XMTok>
              <XMTok font="italic" role="FUNCTION">f</XMTok>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex6">
        <Math mode="display" tex="Df(a)" text="(D@(f))@(a)" xml:id="S2.Ex6.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMRef idref="S2.Ex6.m1.2"/>
                <XMRef idref="S2.Ex6.m1.1"/>
              </XMApp>
              <XMApp>
                <XMApp xml:id="S2.Ex6.m1.2">
                  <XMTok font="italic" role="OPERATOR">D</XMTok>
                  <XMTok font="italic" role="FUNCTION">f</XMTok>
                </XMApp>
                <XMWrap>
                  <XMTok role="OPEN" stretchy="false">(</XMTok>
                  <XMTok font="italic" role="ID" xml:id="S2.Ex6.m1.1">a</XMTok>
                  <XMTok role="CLOSE" stretchy="false">)</XMTok>
                </XMWrap>
              </XMApp>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex7">
        <Math mode="display" tex="DGHf" text="D@(G@(H@(f)))" xml:id="S2.Ex7.m1">
          <XMath>
            <XMApp>
              <XMTok font="italic" role="OPERATOR">D</XMTok>
              <XMApp>
                <XMTok font="italic" role="OPERATOR">G</XMTok>
                <XMApp>
                  <XMTok font="italic" role="OPERATOR">H</XMTok>
                  <XMTok font="italic" role="FUNCTION">f</XMTok>
                </XMApp>
              </XMApp>
            </XMApp>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex8">
        <Math mode="display" tex="DGHf(a)" text="(D@(G@(H@(f))))@(a)" xml:id="S2.Ex8.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMRef idref="S2.Ex8.m1.2"/>
                <XMRef idref="S2.Ex8.m1.1"/>
              </XMApp>
              <XMApp>
                <XMApp xml:id="S2.Ex8.m1.2">
                  <XMTok font="italic" role="OPERATOR">D</XMTok>
                  <XMApp>
                    <XMTok font="italic" role="OPERATOR">G</XMTok>
                    <XMApp>
                      <XMTok font="italic" role="OPERATOR">H</XMTok>
                      <XMTok font="italic" role="FUNCTION">f</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
                <XMWrap>
                  <XMTok role="OPEN" stretchy="false">(</XMTok>
                  <XMTok font="italic" role="ID" xml:id="S2.Ex8.m1.1">a</XMTok>
                  <XMTok role="CLOSE" stretchy="false">)</XMTok>
                </XMWrap>
              </XMApp>
            </XMDual>
          </XMath>
        </Math>
      </equation>
      <equation xml:id="S2.Ex9">
        <Math mode="display" tex="D(a)(b)" text="(D@(a))@(b)" xml:id="S2.Ex9.m1">
          <XMath>
            <XMDual>
              <XMApp>
                <XMRef idref="S2.Ex9.m1.4"/>
                <XMRef idref="S2.Ex9.m1.3"/>
              </XMApp>
              <XMApp>
                <XMDual xml:id="S2.Ex9.m1.4">
                  <XMApp>
                    <XMRef idref="S2.Ex9.m1.1"/>
                    <XMRef idref="S2.Ex9.m1.2"/>
                  </XMApp>
                  <XMApp>
                    <XMTok font="italic" role="OPERATOR" xml:id="S2.Ex9.m1.1">D</XMTok>
                    <XMWrap>
                      <XMTok role="OPEN" stretchy="false">(</XMTok>
                      <XMTok font="italic" role="ID" xml:id="S2.Ex9.m1.2">a</XMTok>
                      <XMTok role="CLOSE" stretchy="false">)</XMTok>
                    </XMWrap>
                  </XMApp>
                </XMDual>
                <XMWrap>
                  <XMTok role="OPEN" stretchy="false">(</XMTok>
                  <XMTok font="italic" role="ID" xml:id="S2.Ex9.m1.3">b</XMTok>
                  <XMTok role="CLOSE" stretchy="false">)</XMTok>
                </XMWrap>
              </XMApp>
            </XMDual>
          </XMath>
        </Math>
      </equation>
    </para>
  </section>
</document>
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