Multiple integral representations for some families of hypergeometric and other polynomials

Abstract

a b s t r a c tThe main objective of this paper is to investigate several general families of hypergeometric and other polynomials and their associated multiple integral representations. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric and other polynomials.

Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations

“…], and Lin et al [6], [9, p. 448 et seq. ], [8] and [7], Liu et al [10] and Srivastava et al [14] and [16]; see also [5]). Here, in our present investigation, we consider the polynomial family defined by where (and throughout this paper) (L s ) abbreviates the array of s parameters…”

Integral representations for the Lagrange polynomials, Shively’s pseudo-Laguerre polynomials, and the generalized Bessel polynomials

“…Srivastava's polynomials S N n (z) and their variants have been widely considered, in recent years, by numerous other workers on the subject (see, for details, González et al [ 11], and Liu et al [13]; see also [21] and the references cited therein).…”

Certain families of multivariable Chan-Chyan-Srivastava polynomials

“…These polynomials include the family of polynomials which were introduced or investigated in [3,13,15,17,19,21,23]. In this paper we introduce r parameter Srivastava polynomials in r variables by inserting new indices.…”