다항 함수

함수 > 특수 함수 > 기타 특수 함수 > 다항 함수

다항 함수

다음 함수는 x에서 나열된 다항식의 n차 값을 구합니다.

• Her(n, x) - 에르미트 다항식 또는 다음 방정식의 해:

<region id="ID0ECPV6" top="76.800000000000011" left="57.600000000000009" height="52.369333557128911" width="196.435" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="11">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <derivative />
            <lambda>
              <boundVars>
                <id xml:space="preserve">x</id>
              </boundVars>
              <id xml:space="preserve">y</id>
            </lambda>
            <degree>
              <real>2</real>
            </degree>
          </apply>
          <apply>
            <mult />
            <apply>
              <scale />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <placeholder />
              </degree>
            </apply>
          </apply>
        </apply>
        <apply>
          <scale />
          <real>2</real>
          <id xml:space="preserve">ny</id>
        </apply>
      </apply>
      <real>0</real>
    </apply>
  </math>
</region>

• Lag(n, x) - 라게르 다항식 또는 다음 방정식의 해:

<region id="ID0ETQV6" top="134.40000000000003" left="57.600000000000009" height="52.369333557128911" width="222.12833333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="13">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <mult />
            <id xml:space="preserve">x</id>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <real>2</real>
              </degree>
            </apply>
          </apply>
          <apply>
            <mult />
            <parens>
              <apply>
                <minus />
                <real>1</real>
                <id xml:space="preserve">x</id>
              </apply>
            </parens>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <placeholder />
              </degree>
            </apply>
          </apply>
        </apply>
        <id xml:space="preserve">ny</id>
      </apply>
      <real>0</real>
    </apply>
  </math>
</region>

• Leg(n, x) - 르장드르 다항식 또는 다음 방정식의 해:

<region id="ID0EESV6" top="192.00000000000003" left="57.600000000000009" height="52.369333557128911" width="295.66166666666669" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="15">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <mult />
            <parens>
              <apply>
                <minus />
                <real>1</real>
                <apply>
                  <pow />
                  <id xml:space="preserve">x</id>
                  <real>2</real>
                </apply>
              </apply>
            </parens>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <real>2</real>
              </degree>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <scale />
              <real>2</real>
              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <placeholder />
              </degree>
            </apply>
          </apply>
        </apply>
        <apply>
          <scale />
          <apply>
            <id xml:space="preserve">n</id>
            <apply>
              <plus />
              <id xml:space="preserve">n</id>
              <real>1</real>
            </apply>
          </apply>
          <id xml:space="preserve">y</id>
        </apply>
      </apply>
      <real>0</real>
    </apply>
  </math>
</region>

• Tcheb(n, x) - 제1종 체비셰프 또는 다음 방정식의 해:

<region id="ID0EVTV6" top="249.60000000000002" left="57.600000000000009" height="52.369333557128911" width="241.09166666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="17">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <scale />
            <parens>
              <apply>
                <minus />
                <real>1</real>
                <apply>
                  <pow />
                  <id xml:space="preserve">x</id>
                  <real>2</real>
                </apply>
              </apply>
            </parens>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <real>2</real>
              </degree>
            </apply>
          </apply>
          <apply>
            <mult />
            <id xml:space="preserve">x</id>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <placeholder />
              </degree>
            </apply>
          </apply>
        </apply>
        <apply>
          <scale />
          <apply>
            <pow />
            <id xml:space="preserve">n</id>
            <real>2</real>
          </apply>
          <id xml:space="preserve">y</id>
        </apply>
      </apply>
      <real>0</real>
    </apply>
  </math>
</region>

• Ucheb(n, x) - 제2종 체비셰프 또는 다음 방정식의 해:

<region id="ID0EGVV6" top="307.20000000000005" left="57.600000000000009" height="52.369333557128911" width="292.11166666666668" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="19">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <minus />
          <apply>
            <scale />
            <parens>
              <apply>
                <minus />
                <real>1</real>
                <apply>
                  <pow />
                  <id xml:space="preserve">x</id>
                  <real>2</real>
                </apply>
              </apply>
            </parens>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <real>2</real>
              </degree>
            </apply>
          </apply>
          <apply>
            <mult />
            <apply>
              <scale />
              <real>3</real>
              <id xml:space="preserve">x</id>
            </apply>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <placeholder />
              </degree>
            </apply>
          </apply>
        </apply>
        <apply>
          <scale />
          <apply>
            <id xml:space="preserve">n</id>
            <apply>
              <plus />
              <id xml:space="preserve">n</id>
              <real>2</real>
            </apply>
          </apply>
          <id xml:space="preserve">y</id>
        </apply>
      </apply>
      <real>0</real>
    </apply>
  </math>
</region>

• Jac(n, a, b, x) - 매개변수가 a 및 b인 야코비 또는 다음 방정식의 해:

<region id="ID0E6WV6" top="364.80000000000007" left="57.600000000000009" height="52.369333557128911" width="448.05166666666668" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="21">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <plus />
          <apply>
            <scale />
            <parens>
              <apply>
                <minus />
                <real>1</real>
                <apply>
                  <pow />
                  <id xml:space="preserve">x</id>
                  <real>2</real>
                </apply>
              </apply>
            </parens>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <real>2</real>
              </degree>
            </apply>
          </apply>
          <apply>
            <scale />
            <parens>
              <apply>
                <minus />
                <apply>
                  <minus />
                  <id xml:space="preserve">b</id>
                  <id xml:space="preserve">a</id>
                </apply>
                <apply>
                  <scale />
                  <parens>
                    <apply>
                      <plus />
                      <apply>
                        <plus />
                        <id xml:space="preserve">a</id>
                        <id xml:space="preserve">b</id>
                      </apply>
                      <real>2</real>
                    </apply>
                  </parens>
                  <id xml:space="preserve">x</id>
                </apply>
              </apply>
            </parens>
            <apply>
              <derivative />
              <lambda>
                <boundVars>
                  <id xml:space="preserve">x</id>
                </boundVars>
                <id xml:space="preserve">y</id>
              </lambda>
              <degree>
                <placeholder />
              </degree>
            </apply>
          </apply>
        </apply>
        <apply>
          <scale />
          <apply>
            <id xml:space="preserve">n</id>
            <apply>
              <plus />
              <apply>
                <plus />
                <apply>
                  <plus />
                  <id xml:space="preserve">n</id>
                  <id xml:space="preserve">a</id>
                </apply>
                <id xml:space="preserve">b</id>
              </apply>
              <real>1</real>
            </apply>
          </apply>
          <id xml:space="preserve">y</id>
        </apply>
      </apply>
      <real>0</real>
    </apply>
  </math>
</region>

체비셰프 및 르장드르 다항식은 특수한 사례의 야코비 다항식입니다.

인수

• n은 음이 아닌 정수입니다.

• x는 실수 스칼라 값입니다.

• a, b는 –1보다 큰 실수 스칼라 값입니다.

관련 항목

기타 특수 함수 정보

예제: 다항 함수

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