A new result for hypergeometric polynomials

Abstract

Abstract. In some recent investigations involving differential operators for generalized Laguerre polynomials, Herman Bavinck (1996) encountered and proved a certain summation formula for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation formula for a class of hypergeometric polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. The general summation formula is also applied to derive the corresponding result for the classical Jacobi polynomials.

Some New Generating Functions for the Modified Laguerre Polynomials

“…where |βt| < 1. In recent years, many researchers have studied multilinear and multilateral generating functions for different type of polynomials, such as Altın et al [1], Chan et al [2], Chen et al [5,6], Dattoil et al [8], Erkus et al [11] and Liu [14], Qureshi et al [25]. Similarly, in [15] Liu et al introduced bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella functions, and in [16] bilateral generating functions for the Erkus-Srivastava polynomials and generalized Lauricella functions were derived.…”