Linearization formulae for certain Jacobi polynomials

Abstract

In this article, some new linearization formulae of products of Jacobi polynomials for certain parameters are derived. These new derived formulae are expressed in terms of hypergeometric functions of unit argument, and they generalize some existing formulae in the literature. With the aid of some standard formulae and also by employing symbolic algebraic computation, and in particular Zeilberger's algorithm, several reduction formulae for summing certain terminating hypergeometric functions of unit argument are given, and hence several linearization formulae of products of Jacobi polynomials for special parameters free of hypergeometric functions are deduced.