Generating relations and multivariable Aleph-function

Abstract

Srivastava and Panda have studied the simple and multiple generating relations concerning the multivariable H-function. The aim of this paper is to derive the various classes of simple and multiple generating relations involving the multivariable Aleph-function. The generating function is used in the theory of numbers, in physics and other fields of mathematics. We see the particular cases concerning the multivariable I-function, the Aleph-function of two variables and the I-function of two variables.

On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions

“…Taking B � 0 in (17) and (18), we get the results in [21]. Also, by using the identity matrix, we can find the scalar case incomplete extended Gamma and Beta functions in [1,[27][28][29][30] as A � αI and B � βI. If A � αI and B � 0, we have Gamma and Beta functions.…”

Application of Jacobi Polynomial and Multivariable Aleph- Function in Heat Conduction in Non-Homogeneous Moving Rectangular Parallelepiped

“…The multivariable Aleph-function is a generalization of the multivariable H-function defined by Srivastava and Panda [14,15]. The multivariable Aleph-function is defined by means of the multiple contour integral [3,7]:…”

On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial

“…ey are used to find certain properties and formulas for numbers and polynomials in a wide variety of research subjects, indeed, in modern combinatorics. One can refer to the extensive work of Srivastava and Manocha [24] for a systematic introduction and several interesting and useful applications of the various methods of obtaining linear, bilinear, bilateral, or mixed multilateral generating functions for a fairly wide variety of sequences of special functions (and polynomials) in one, two, and more variables, among much abundant literature; in this regard, in fact, a remarkable large number of generating functions involving a variety of special functions have been developed by many authors (see, e.g., [13,[25][26][27]). Here, we present some generating functions involving the following family of the extended Gauss hypergeometric matrix functions: Theorem 1.…”