Some properties of generalized multiple Hermite polynomials

Abstract

a b s t r a c tThe purpose of this paper is to introduce and discuss a more general class of multiple Hermite polynomials. In this work, the explicit forms, operational formulas and a recurrence relation are obtained. Furthermore, we derive several families of bilinear, bilateral and mixed multilateral finite series relationships and generating functions for the generalized multiple Hermite polynomials.

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

“…Taking into account these equalities in (13) leads to the desired third order linear differential equation .…”

“…In literature, there are numerous investigations to obtain generating functions and recurrence relations satisfied by special functions and polynomials (see [3,4,5,6,7,8,9,10,11,12,13,14,18]). It is possible to derive a recurrence relation by using a generating function.…”

“…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.…”

Solution of Problems in Calculus of Variations Using Parameterization Technique

“…Hermite polynomials and its applications have been studied for long and still attract attention. One can refer a long and list of books and journals for advanced knowledge of Hermite polynomials and its extension, for example [9], for books, and [10], [11]and [12] for journals. Definition [13] The nth Hermite polynomials denoted by…”

A generalization of Hermite polynomials

“…One can refer a long list of books and journals for advanced knowledge of Hermite polynomials and its extensions, for example [7] and [6], for books and [2], [4] , [5], [7], [8], [9], [10] and [11] for journals. Based on a generalized hypergeometric function, we introduce here a generalization of the Hermite polynomials that provide natural extensions of basic results involving the Hermite polynomials as a study of the Laguerre polynomials in [3].…”