Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals

Howard S. Cohl, Connor MacKenzie, Hans Volkmer

Published 2013-02-11Version 1

We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using connection relations with one free parameter for these orthogonal polynomials. We also use orthogonality relations to determine corresponding definite integrals.