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.
Citation: Journal of Mathematical Analysis and Applications
Pub Type: Journals
Orthogonal polynomials, Generating functions, Connection coefficients, Generalized hypergeometric functions, Eigenfunction expansions, Definite integrals