예제: 타원 적분 함수

함수 > 기호 함수 > 예제: 타원 적분 함수

예제: 타원 적분 함수

타원 적분 함수의 도함수 계산하기

• 제1종 완전 타원 적분:

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  <math resultRef="16">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">m</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticK</id>
            <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
          </apply>
        </lambda>
        <degree>
          <placeholder />
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <plus />
            <apply>
              <neg />
              <apply>
                <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
                <id xml:space="preserve" labels="VARIABLE">m</id>
              </apply>
            </apply>
            <apply>
              <mult />
              <parens>
                <apply>
                  <minus />
                  <real>1</real>
                  <id xml:space="preserve" labels="VARIABLE">m</id>
                </apply>
              </parens>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">ellipticK</id>
                <id xml:space="preserve" labels="VARIABLE">m</id>
              </apply>
            </apply>
          </apply>
          <apply>
            <minus />
            <apply>
              <mult />
              <real>2</real>
              <apply>
                <pow />
                <id xml:space="preserve" labels="VARIABLE">m</id>
                <real>2</real>
              </apply>
            </apply>
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="VARIABLE">m</id>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

• 제1종 완전 타원 적분의 2차 도함수:

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  <math resultRef="17">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">m</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticK</id>
            <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
          </apply>
        </lambda>
        <degree>
          <real>2</real>
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <plus />
            <apply>
              <mult />
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <mult />
                    <real>4</real>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </apply>
                  <real>2</real>
                </apply>
              </parens>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
                <id xml:space="preserve" labels="VARIABLE">m</id>
              </apply>
            </apply>
            <apply>
              <mult />
              <parens>
                <apply>
                  <plus />
                  <apply>
                    <minus />
                    <apply>
                      <mult />
                      <real>3</real>
                      <apply>
                        <pow />
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                        <real>2</real>
                      </apply>
                    </apply>
                    <apply>
                      <mult />
                      <real>5</real>
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                    </apply>
                  </apply>
                  <real>2</real>
                </apply>
              </parens>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">ellipticK</id>
                <id xml:space="preserve" labels="VARIABLE">m</id>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus />
            <apply>
              <minus />
              <apply>
                <mult />
                <real>4</real>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE">m</id>
                  <real>4</real>
                </apply>
              </apply>
              <apply>
                <mult />
                <real>8</real>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE">m</id>
                  <real>3</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <mult />
              <real>4</real>
              <apply>
                <pow />
                <id xml:space="preserve" labels="VARIABLE">m</id>
                <real>2</real>
              </apply>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 제1종 불완전 타원 적분의 m에 의한 1차 도함수:

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  <math resultRef="18">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">m</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
            <sequence>
              <id xml:space="preserve">z</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
            </sequence>
          </apply>
        </lambda>
        <degree>
          <placeholder />
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <neg />
            <apply>
              <div />
              <apply>
                <plus />
                <apply>
                  <mult />
                  <parens>
                    <apply>
                      <minus />
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                      <real>1</real>
                    </apply>
                  </parens>
                  <apply>
                    <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
                    <sequence>
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                    </sequence>
                  </apply>
                </apply>
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
                  <sequence>
                    <id xml:space="preserve" labels="VARIABLE">z</id>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </sequence>
                </apply>
              </apply>
              <apply>
                <minus />
                <apply>
                  <mult />
                  <real>2</real>
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                    <real>2</real>
                  </apply>
                </apply>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="VARIABLE">m</id>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <div />
            <apply>
              <mult />
              <id xml:space="preserve" labels="VARIABLE">z</id>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <mult />
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </apply>
                  <real>2</real>
                </apply>
              </parens>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <parens>
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">z</id>
                          <real>2</real>
                        </apply>
                      </apply>
                    </parens>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 제1종 불완전 타원 적분의 z에 의한 1차 도함수:

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  <math resultRef="19">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">z</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
            <sequence>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">z</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
            </sequence>
          </apply>
        </lambda>
        <degree>
          <placeholder />
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <div />
          <real>1</real>
          <apply>
            <mult />
            <apply>
              <nthRoot />
              <placeholder />
              <apply>
                <plus />
                <apply>
                  <neg />
                  <parens>
                    <apply>
                      <mult />
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                      <apply>
                        <pow />
                        <id xml:space="preserve" labels="VARIABLE">z</id>
                        <real>2</real>
                      </apply>
                    </apply>
                  </parens>
                </apply>
                <real>1</real>
              </apply>
            </apply>
            <apply>
              <nthRoot />
              <placeholder />
              <apply>
                <plus />
                <apply>
                  <neg />
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="VARIABLE">z</id>
                    <real>2</real>
                  </apply>
                </apply>
                <real>1</real>
              </apply>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 제1종 불완전 타원 적분의 m에 의한 2차 도함수:

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  <math resultRef="20">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">m</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
            <sequence>
              <id xml:space="preserve">z</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
            </sequence>
          </apply>
        </lambda>
        <degree>
          <real>2</real>
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <minus />
          <apply>
            <div />
            <apply>
              <plus />
              <apply>
                <mult />
                <parens>
                  <apply>
                    <plus />
                    <apply>
                      <minus />
                      <apply>
                        <mult />
                        <real>3</real>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                          <real>2</real>
                        </apply>
                      </apply>
                      <apply>
                        <mult />
                        <real>5</real>
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                      </apply>
                    </apply>
                    <real>2</real>
                  </apply>
                </parens>
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
                  <sequence>
                    <id xml:space="preserve" labels="VARIABLE">z</id>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </sequence>
                </apply>
              </apply>
              <apply>
                <mult />
                <parens>
                  <apply>
                    <minus />
                    <apply>
                      <mult />
                      <real>4</real>
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                    </apply>
                    <real>2</real>
                  </apply>
                </parens>
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
                  <sequence>
                    <id xml:space="preserve" labels="VARIABLE">z</id>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </sequence>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus />
              <apply>
                <minus />
                <apply>
                  <mult />
                  <real>4</real>
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                    <real>4</real>
                  </apply>
                </apply>
                <apply>
                  <mult />
                  <real>8</real>
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                    <real>3</real>
                  </apply>
                </apply>
              </apply>
              <apply>
                <mult />
                <real>4</real>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE">m</id>
                  <real>2</real>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <div />
            <apply>
              <mult />
              <parens>
                <apply>
                  <plus />
                  <apply>
                    <mult />
                    <parens>
                      <apply>
                        <minus />
                        <apply>
                          <mult />
                          <real>4</real>
                          <apply>
                            <pow />
                            <id xml:space="preserve" labels="VARIABLE">m</id>
                            <real>2</real>
                          </apply>
                        </apply>
                        <apply>
                          <mult />
                          <real>2</real>
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                        </apply>
                      </apply>
                    </parens>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>3</real>
                    </apply>
                  </apply>
                  <apply>
                    <mult />
                    <parens>
                      <apply>
                        <minus />
                        <real>1</real>
                        <apply>
                          <mult />
                          <real>3</real>
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                        </apply>
                      </apply>
                    </parens>
                    <id xml:space="preserve" labels="VARIABLE">z</id>
                  </apply>
                </apply>
              </parens>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <mult />
              <parens>
                <apply>
                  <plus />
                  <apply>
                    <mult />
                    <parens>
                      <apply>
                        <plus />
                        <apply>
                          <minus />
                          <apply>
                            <mult />
                            <real>4</real>
                            <apply>
                              <pow />
                              <id xml:space="preserve" labels="VARIABLE">m</id>
                              <real>4</real>
                            </apply>
                          </apply>
                          <apply>
                            <mult />
                            <real>8</real>
                            <apply>
                              <pow />
                              <id xml:space="preserve" labels="VARIABLE">m</id>
                              <real>3</real>
                            </apply>
                          </apply>
                        </apply>
                        <apply>
                          <mult />
                          <real>4</real>
                          <apply>
                            <pow />
                            <id xml:space="preserve" labels="VARIABLE">m</id>
                            <real>2</real>
                          </apply>
                        </apply>
                      </apply>
                    </parens>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                  <parens>
                    <apply>
                      <minus />
                      <apply>
                        <minus />
                        <apply>
                          <mult />
                          <real>8</real>
                          <apply>
                            <pow />
                            <id xml:space="preserve" labels="VARIABLE">m</id>
                            <real>2</real>
                          </apply>
                        </apply>
                        <apply>
                          <mult />
                          <real>4</real>
                          <apply>
                            <pow />
                            <id xml:space="preserve" labels="VARIABLE">m</id>
                            <real>3</real>
                          </apply>
                        </apply>
                      </apply>
                      <apply>
                        <mult />
                        <real>4</real>
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                      </apply>
                    </apply>
                  </parens>
                </apply>
              </parens>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <parens>
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">z</id>
                          <real>2</real>
                        </apply>
                      </apply>
                    </parens>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 제2종 불완전 타원 적분의 m 및 z에 의한 1차 도함수:

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  <math resultRef="21">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">m</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
            <sequence>
              <id xml:space="preserve">z</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
            </sequence>
          </apply>
        </lambda>
        <degree>
          <placeholder />
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <plus />
            <apply>
              <neg />
              <apply>
                <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
                <sequence>
                  <id xml:space="preserve" labels="VARIABLE">z</id>
                  <id xml:space="preserve" labels="VARIABLE">m</id>
                </sequence>
              </apply>
            </apply>
            <apply>
              <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
              <sequence>
                <id xml:space="preserve" labels="VARIABLE">z</id>
                <id xml:space="preserve" labels="VARIABLE">m</id>
              </sequence>
            </apply>
          </apply>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve" labels="VARIABLE">m</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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  <math resultRef="22">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <derivative />
        <lambda>
          <boundVars>
            <id xml:space="preserve">z</id>
          </boundVars>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
            <sequence>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">z</id>
              <id xml:space="preserve" labels="VARIABLE" label-is-contextual="true">m</id>
            </sequence>
          </apply>
        </lambda>
        <degree>
          <placeholder />
        </degree>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <plus />
              <apply>
                <neg />
                <parens>
                  <apply>
                    <mult />
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                </parens>
              </apply>
              <real>1</real>
            </apply>
          </apply>
          <apply>
            <nthRoot />
            <placeholder />
            <apply>
              <plus />
              <apply>
                <neg />
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE">z</id>
                  <real>2</real>
                </apply>
              </apply>
              <real>1</real>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 제3종 불완전 타원 적분의 m, n, z에 의한 1차 도함수:

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            <id xml:space="preserve">m</id>
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                    <minus />
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                    <real>1</real>
                  </apply>
                </parens>
                <apply>
                  <id xml:space="preserve" labels="FUNCTION">ellipticPi</id>
                  <sequence>
                    <id xml:space="preserve" labels="VARIABLE">z</id>
                    <id xml:space="preserve" labels="VARIABLE">n</id>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
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                <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
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                  <id xml:space="preserve" labels="VARIABLE">m</id>
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            </apply>
            <apply>
              <plus />
              <apply>
                <mult />
                <parens>
                  <apply>
                    <minus />
                    <apply>
                      <mult />
                      <real>2</real>
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                    </apply>
                    <real>2</real>
                  </apply>
                </parens>
                <id xml:space="preserve" labels="VARIABLE">n</id>
              </apply>
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </apply>
                  <apply>
                    <mult />
                    <real>2</real>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">m</id>
                      <real>2</real>
                    </apply>
                  </apply>
                </apply>
              </parens>
            </apply>
          </apply>
          <apply>
            <div />
            <apply>
              <mult />
              <apply>
                <mult />
                <id xml:space="preserve" labels="VARIABLE">m</id>
                <id xml:space="preserve" labels="VARIABLE">z</id>
              </apply>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <mult />
              <parens>
                <apply>
                  <plus />
                  <apply>
                    <mult />
                    <parens>
                      <apply>
                        <minus />
                        <apply>
                          <mult />
                          <real>2</real>
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                        </apply>
                        <real>2</real>
                      </apply>
                    </parens>
                    <id xml:space="preserve" labels="VARIABLE">n</id>
                  </apply>
                  <parens>
                    <apply>
                      <minus />
                      <apply>
                        <mult />
                        <real>2</real>
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                      </apply>
                      <apply>
                        <mult />
                        <real>2</real>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                          <real>2</real>
                        </apply>
                      </apply>
                    </apply>
                  </parens>
                </apply>
              </parens>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <parens>
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">z</id>
                          <real>2</real>
                        </apply>
                      </apply>
                    </parens>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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                        <real>2</real>
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                      <id xml:space="preserve" labels="VARIABLE">m</id>
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                    <id xml:space="preserve" labels="FUNCTION">ellipticPi</id>
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                      <id xml:space="preserve" labels="VARIABLE">m</id>
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                <apply>
                  <plus />
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                    <mult />
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                        <minus />
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                        <id xml:space="preserve" labels="VARIABLE">n</id>
                      </apply>
                    </parens>
                    <apply>
                      <id xml:space="preserve" labels="FUNCTION">ellipticF</id>
                      <sequence>
                        <id xml:space="preserve" labels="VARIABLE">z</id>
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                      </sequence>
                    </apply>
                  </apply>
                  <apply>
                    <mult />
                    <id xml:space="preserve" labels="VARIABLE">n</id>
                    <apply>
                      <id xml:space="preserve" labels="FUNCTION">ellipticE</id>
                      <sequence>
                        <id xml:space="preserve" labels="VARIABLE">z</id>
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                      </sequence>
                    </apply>
                  </apply>
                </apply>
              </apply>
              <apply>
                <plus />
                <apply>
                  <minus />
                  <apply>
                    <mult />
                    <real>2</real>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">n</id>
                      <real>3</real>
                    </apply>
                  </apply>
                  <apply>
                    <mult />
                    <parens>
                      <apply>
                        <plus />
                        <apply>
                          <mult />
                          <real>2</real>
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                        </apply>
                        <real>2</real>
                      </apply>
                    </parens>
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">n</id>
                      <real>2</real>
                    </apply>
                  </apply>
                </apply>
                <apply>
                  <mult />
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </apply>
                  <id xml:space="preserve" labels="VARIABLE">n</id>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <div />
            <apply>
              <mult />
              <apply>
                <mult />
                <apply>
                  <mult />
                  <id xml:space="preserve" labels="VARIABLE">n</id>
                  <id xml:space="preserve" labels="VARIABLE">z</id>
                </apply>
                <apply>
                  <nthRoot />
                  <placeholder />
                  <apply>
                    <plus />
                    <apply>
                      <neg />
                      <parens>
                        <apply>
                          <mult />
                          <id xml:space="preserve" labels="VARIABLE">m</id>
                          <apply>
                            <pow />
                            <id xml:space="preserve" labels="VARIABLE">z</id>
                            <real>2</real>
                          </apply>
                        </apply>
                      </parens>
                    </apply>
                    <real>1</real>
                  </apply>
                </apply>
              </apply>
              <apply>
                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
            <apply>
              <plus />
              <apply>
                <mult />
                <parens>
                  <apply>
                    <plus />
                    <apply>
                      <minus />
                      <apply>
                        <mult />
                        <real>2</real>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">n</id>
                          <real>3</real>
                        </apply>
                      </apply>
                      <apply>
                        <mult />
                        <parens>
                          <apply>
                            <plus />
                            <apply>
                              <mult />
                              <real>2</real>
                              <id xml:space="preserve" labels="VARIABLE">m</id>
                            </apply>
                            <real>2</real>
                          </apply>
                        </parens>
                        <apply>
                          <pow />
                          <id xml:space="preserve" labels="VARIABLE">n</id>
                          <real>2</real>
                        </apply>
                      </apply>
                    </apply>
                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <real>2</real>
                        <id xml:space="preserve" labels="VARIABLE">m</id>
                      </apply>
                      <id xml:space="preserve" labels="VARIABLE">n</id>
                    </apply>
                  </apply>
                </parens>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="VARIABLE">z</id>
                  <real>2</real>
                </apply>
              </apply>
              <parens>
                <apply>
                  <minus />
                  <apply>
                    <minus />
                    <apply>
                      <mult />
                      <parens>
                        <apply>
                          <plus />
                          <apply>
                            <mult />
                            <real>2</real>
                            <id xml:space="preserve" labels="VARIABLE">m</id>
                          </apply>
                          <real>2</real>
                        </apply>
                      </parens>
                      <id xml:space="preserve" labels="VARIABLE">n</id>
                    </apply>
                    <apply>
                      <mult />
                      <real>2</real>
                      <apply>
                        <pow />
                        <id xml:space="preserve" labels="VARIABLE">n</id>
                        <real>2</real>
                      </apply>
                    </apply>
                  </apply>
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="VARIABLE">m</id>
                  </apply>
                </apply>
              </parens>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
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                      <id xml:space="preserve" labels="VARIABLE">n</id>
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                          <id xml:space="preserve" labels="VARIABLE">m</id>
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                    <real>1</real>
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                <nthRoot />
                <placeholder />
                <apply>
                  <plus />
                  <apply>
                    <neg />
                    <apply>
                      <pow />
                      <id xml:space="preserve" labels="VARIABLE">z</id>
                      <real>2</real>
                    </apply>
                  </apply>
                  <real>1</real>
                </apply>
              </apply>
            </apply>
          </apply>
        </apply>
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    </symEval>
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타원 적분 함수를 숫자로 계산하기

• assume 키워드를 사용합니다.

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          <id xml:space="preserve">m</id>
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      </apply>
      <command>
        <sequence>
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              <equal />
              <id xml:space="preserve">z</id>
              <real>1</real>
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          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">m</id>
            <real>0</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
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          <id xml:space="preserve" labels="CONSTANT">π</id>
          <real>2</real>
        </apply>
      </symResult>
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함수 인수도 설정할 수 있습니다.

m이 0에 가까워질 때 ellipticF의 극한을 계산합니다.

• float 키워드를 사용합니다.

• ellipticK는 m=1일 때 특이점을 가집니다. m>1의 경우 결과는 복소수입니다.

• 벡터의 ellipticK를 계산합니다.

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      <apply>
        <id xml:space="preserve" labels="FUNCTION">ellipticK</id>
        <matrix rows="4" cols="1">
          <real>-0.5</real>
          <real>0.5</real>
          <real>1</real>
          <real>1.5</real>
        </matrix>
      </apply>
      <command>
        <placeholder />
      </command>
      <symResult>
        <matrix rows="4" cols="1">
          <real>1.415737208425956295</real>
          <real>1.8540746773013719184</real>
          <id xml:space="preserve" labels="CONSTANT">∞</id>
          <apply>
            <minus />
            <real>1.6566381702365939876</real>
            <imag symbol="i">1.4157372084259560729</imag>
          </apply>
        </matrix>
      </symResult>
    </symEval>
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