The classical Gauss hypergeometric function and the Kumar confluent are defined using a Pochammer symbol , factorial function. This research paper will present two-parameter Pochhammer symbol, discuss some of its properties such as recursive formulae integral representation. In addition, generalized functions new were also discussed.

We prove a duality relation for the generalized basic hypergeometric functions. It forms q-extension of recent result second- and third-named authors generalizes both q-hypergeometric identity due to author (jointly with Feng Yang) Heine’s $${}_2\phi _{1}$$ function Suzuki. further explore various consequences our leading several presumably new multi-term relations terminating non-terminating s...

We deduce an explicit representation for the coefficients in a finite expansion of a certain class of generalized hypergeometric functions that contain multiple pairs of numeratorial and denominatorial parameters differing by positive integers. The expansion alluded to is given in terms of these coefficients and hypergeometric functions of lower order. Applications to Euler and Kummer-type tran...

The incomplete gamma function and incomplete beta function are important special functions in statistics. In modern theory of special functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles [1, Chap 2]. However, domains of integrations of these incomplete functions are not cycles. Solutions of A-hypergeometric systems ([3], [7, p.221]) have integral repr...

Formulas and identities involving many well-known special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) play important rôles in themselves and in their diverse applications. Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing some (presumably new) gene...

Abstract. This paper deals with the study of the generalized hypergeometric matrix function and obtains some of its properties. We rephrase some results from the previous (earlier) works that will be used in this study. We get the hypergeometric matrix function representation, matrix differential equation, generating matrix functions, bilinear generating matrix functions, matrix recurrence rela...