Search

In this paper, we introduce ten new quadruple hypergeometric series. We also obtain their various properties such that integral representations, fractional derivatives, N-fractional connections, operational relations and generating functions. [ABSTRACT FROM AUTHOR]

In this paper, the higher-order type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some p-adic integral representations of not only higher-order type 2 Daehee polynomials and numbers but also type 2 Daehee polynomials and numbers are acquired. Several identities and relations related to both central factorial numbers of the second kind and Stirling numbers of the first and second kinds are investigated. Moreover, the conjugate higher-order type 2 Daehee polynomials are considered and some correlations covering the type 2 Daehee polynomials of order β and the conjugate higher-order type 2 Daehee polynomials are attained. [ABSTRACT FROM AUTHOR]

In this paper, the higher-order type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some p-adic integral representations of not only higher-order type 2 Daehee polynomials and numbers but also type 2 Daehee polynomials and numbers are acquired. Several identities and relations related to both central factorial numbers of the second kind and Stirling numbers of the first and second kinds are investigated. Moreover, the conjugate higher-order type 2 Daehee polynomials are considered and some correlations covering the type 2 Daehee polynomials of order β and the conjugate higher-order type 2 Daehee polynomials are attained. [ABSTRACT FROM AUTHOR]

Various integral representations of hypergeometric functions have been introduced and investigated due to their important applications in divers fields. In this article, we define some new Eulertype integral representations for the Horn's functions of two variables G1, G2, G3 and H1. [ABSTRACT FROM AUTHOR]

Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In this manuscript, our goal is to initiate a new quadruple hypergeometric function denoted by X 84 4 , and then, we ensure the existence of solutions of systems of partial differential equations for this function. We also establish some integral representations involving the quadruple hypergeometric function X 84 4 . [ABSTRACT FROM AUTHOR]

Generating functions plays an essential role in the investigation of several useful properties of the sequences which they generate. In this paper, we establish certain generating relations, involving some quadruple hypergeometric functions introduced by Bin-Saad and Younis. Some interesting special cases of our main results are also considered. [ABSTRACT FROM AUTHOR]

In the present work, we establish a new integral representations of Euler type for the quadruple hypergeometric functions Xi(4)(.), i = 38, 40, 45, 48, 50. We obtain some operational relations include these quadruple functions. [ABSTRACT FROM AUTHOR]

A new class of quadruple hypergeometric series is presented. We also give integral representations of Euler- type and Laplace-type for the new class of series. [ABSTRACT FROM AUTHOR]

While investigating the Exton's list of twenty one hyper-geometric functions of four variables and the Sharma's and Parihar's list of eighty three hyper-geometric functions of four variables, we noticed existence of new hyper-geometric series of four variables. The principal object of this paper is to introduce new hyper-geometric series of four variables and present a natural further step toward the mathematical integral presentation concerning these new series of four variables. Integral representations of Euler type and Laplace type involving Appell's hyper-geometric functions and the Horn's series of two variables, Exton's and Lauricella's triple functions and Sharma and Parihar hyper-geometric functions of four variables are established. [ABSTRACT FROM AUTHOR]

In this paper, we define some new quadruple hypergeometric functions, which we denoted by X(4)i (i = 31, 32, ..., 50). Then, we obtain its integral representations of Euler-type and Laplace-type. [ABSTRACT FROM AUTHOR]