ON SOME NEW GENERATING FUNCTIONS OF HYPERGEOMETRIC POLYNOMIALS

Abstract

This paper contains mainly three theorems involving Kampe´ de Fe´riet’s function F ⁽²⁾ and expressed in terms of single and double Laplace and Beta inte- grals. The theorems,  in turn,  yield,  as special cases,  a number of linear,  bilin- ear and bilateral generating functions of generalized polynomials of Rice, Jacobi polynomials, Ultraspherical, Generalized Laguerre, Bedient polynomials and other polynomials hypergeometric in nature. One variable special cases of generalized polynomials are useful in several applied problems.