Gegenbauer polynomials

In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α)n(x) are orthogonal polynomials on the interval with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer.