Linearization of the Product of Jacobi Polynomials. I

Abstract

Let P_n^(α,β) be the Jacobi polynomial of degree n, order (α,β), α,β > – 1, defined by [9, p. 67], and let R_n^(α,β)(x) = P_n^(α,β)(x)/P_n(αβ)(1). Then for n ≧ m, where Since R_n^{(α, β)}(l) = 1, it follows that (1) It is known that if (the ultraspherical case) or if α = β + 1, then α = β + 1, then g(k, n, m) ≧ 0.