The Laguerre polynomials in several variables

Abstract

ABSTRACT. In this paper, we give some relations between multivariable Laguerre polynomials and other well-known multivariable polynomials. We get various families of multilinear and multilateral generating functions for these polynomials. Some special cases are also presented.

Extended Multivariable Hypergeometric Functions

“…In this section, we derive several families of multilinear and multilateral generating function for multivariable hypergeometric functions defined by (2.1) by using the similar method considered in [1,2]. a k (λ) n−pk (k) E (r) λ + n − pk, β k+1 , ..., β r ; γ 1 , ..., γ r ; x 1 , ..., x r Ω µ+ψk (y 1 , ..., y s ) ξ k (n − pk)!…”

A new family of analytic functions defined by means of Rodrigues type formula

“…In this section, we try to derive many families of bilinear and bilateral generating functions for the family of analytic functions given by ( 4) by means of the similar method presented in [2,4,5,6,7,8,9,10,11,12,13,18]. For this purpose, let's begin the following theorem.…”

“…Moreover, a class of multivariable polynomials was studied in [11]. Now, let's consider a family of analytic functions which is more general than the polynomials (2) . Assume that ϕ 1 (x) , ϕ 2 (x) and ψ (x) are analytic functions.…”

Meixner Polinomlarının Bazı Yeni Özellikleri

“…which are generated by (1.1) and given by (1.2) using the similar method considered in (see [5], [10]- [16], [19], [21]- [25]).…”