M. A. PATHAN, M. I. QURESHI and N. U. KHAN

Some multivariable bilateral generating relations involving Jacobi polynomials

Pages: 229-244
Received: 7 May 2001   
Revised: 18 October 2001
Mathematics Subject Classification (2000): 33C45 - 33C55 - 33C64 - 33C65 - 33C70 - 33C99

Abstract: In this paper the authors prove a general theorem on generating relation for a certain seqeunce of functions. Many formulas involving the families of generating functions for the Jacobi and the so called extended Jacobi (or Fujiwara) polynomials given by Sharma and Manocha [14], Manocha [13], Sharma [19], Sharma and Mittal [20], Manocha and Srivastava [23],[24], Pittaluga, Sacripante and Srivastava [17] are shown here to be special cases of a general class of a generating function involving Jacobi (or Fujiwara) polynomials and multiple hypergeometric series of several variables. It is then shown how the main result can be applied to derive a large number of generating functions involving hypergeometric functions of Appell, Lauricella, Kampé de Fériet, Srivastava, Pathan, Exton, Chandel, Khichi, Karlsson, Chandel-Gupta, Pandey, Dhawan and other multiple Gaussian hypergeometric functions scatterred in the literature of special functions.