Plot of <a href="https://en.wikipedia.org/wiki/Gegenbauer_polynomials" class="extiw" title="en:Gegenbauer polynomials">Gegenbauer polynomials</a> C<sub>n</sub><sup>(α)</sup> with n=3 in the interval [−2.1, 2.1]:
<ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=C_{3}^{(0)}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msubsup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y(x)=C_{3}^{(0)}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51e1b3598f3bd507b62df44983cb90d8b5ba6ae3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:11.524ex; height:3.676ex;" alt="{\displaystyle y(x)=C_{3}^{(0)}}"></span></li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=C_{3}^{(1)}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></msubsup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y(x)=C_{3}^{(1)}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76e182365da0df60cf9d7fc02c5d5960b3e7e3c2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:11.524ex; height:3.676ex;" alt="{\displaystyle y(x)=C_{3}^{(1)}}"></span></li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=C_{3}^{(2)}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo></mrow></msubsup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y(x)=C_{3}^{(2)}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b7f248fb978f2f0abe22eae3f103c5d956edfe9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:11.524ex; height:3.676ex;" alt="{\displaystyle y(x)=C_{3}^{(2)}}"></span></li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=C_{3}^{(3)}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow></msubsup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y(x)=C_{3}^{(3)}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd5d6ae3ab42819bb1313c19591c9eeb4fb3e30f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:11.524ex; height:3.676ex;" alt="{\displaystyle y(x)=C_{3}^{(3)}}"></span></li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=C_{3}^{(4)}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></mrow></msubsup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y(x)=C_{3}^{(4)}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dc7cd803acd736a5166f470b7af65b6a7091b3d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:11.524ex; height:3.676ex;" alt="{\displaystyle y(x)=C_{3}^{(4)}}"></span></li>
<li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(x)=C_{3}^{(5)}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">(</mo><mn>5</mn><mo stretchy="false">)</mo></mrow></msubsup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y(x)=C_{3}^{(5)}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04db5807cd1d5394be60d390b3527ecd5171b95b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:11.524ex; height:3.676ex;" alt="{\displaystyle y(x)=C_{3}^{(5)}}"></span></li></ul>
<a href="//commons.wikimedia.org/wiki/User:Geek3" title="User:Geek3">Geek3</a>
CC BY 3.0
<span class="int-own-work" lang="en">Own work</span>