Linearization of the Product of Jacobi Polynomials. II

Abstract

Let [ 3 , p. 170, (16)] (1.1) denote the Jacobi polynomial of order (α, β), α, β > – 1, and let g(k, m, n; α, β) be denned by (1.2) where R n (α, β) (x) = P n (α, β) (x)/P n (α, β) (1). It is well known [ 1; 2; 4; 5; 6 ] that the harmonic analysis of Jacobi polynomials depends, at crucial points, on the answers to the following two questions. Question 1. For which (α, β) do we have (1.3) Question 2. For which (α, β) do we have (1.4) where G depends only on (α, β)?