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Gegenbauer polynomials
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, Gegenbauer polynomials or ultraspherical polynomials <i>C</i>(α)<i>n</i>(<i>x</i>) are <a href="/facts/Orthogonal_polynomials/9cyRbDYU">orthogonal polynomials</a> on the interval [−1,1] with respect to the <a href="/facts/Weight_function/YNJL7o99">weight function</a> (1 − <i>x</i>2)<i>α</i>–1/2. They generalize <a href="/facts/Legendre_polynomials/nDvV4em0">Legendre polynomials</a> and <a href="/facts/Chebyshev_polynomials/HoBINqgC">Chebyshev polynomials</a>, and are special cases of <a href="/facts/Jacobi_polynomials/5oKJKB1W">Jacobi polynomials</a>. They are named after <a href="/facts/Leopold_Gegenbauer/mpUKYKz7">Leopold Gegenbauer</a>. </p>