In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P(α, β)
n(x) are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight (1 − x)(1 + x) on the interval [−1, 1]. The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials.