Contiguous Function Relations for k-Hypergeometric Functions

Abstract

In this research work, our aim is to determine the contiguous function relations for -hypergeometric functions with one parameter corresponding to Gauss fifteen contiguous function relations for hypergeometric functions and also obtain contiguous function relations for two parameters. Throughout in this research paper, we find out the contiguous function relations for both the cases in terms of a new parameter > 0. Obviously if → 1, then the contiguous function relations for -hypergeometric functions are Gauss contiguous function relations.

Some results on (p, k)-extension of the hypergeometric functions

“…The k-analogue of theta operator kΘ as given in [18,19,25], takes the form kΘ = k ξ dξ . This operator has the particularly pleasant property that kΘξ m = kmξ m , which makes it handy to be used on power series.…”

“…In particular, Diaz and Pariguan [16] introduced the k-analogue of gamma, beta and hypergeometric functions and proved a number of their properties. Since that period, many different results concerning the k-hypergeometric function and related functions have been considered by many researchers, for instance, Agarwal et al [17], Mubeen et al [18][19][20], Rahman et al [21], Chinra et al [22], Korkmaz-Duzgun and Erkus-Duman [23], Nisar et al [24], Li and Dong [25], Yilmaz et al [26] and Yilmazer and Ali [27].…”

New Generalizations of Exponential Distribution with Applications

“…More recently, Rahman et al [7] (for more details see [8][9][10][11][12][13][14][15][16]) have defined -gamma and -beta distributions and their MGFs as follows.…”

Contiguous Function Relations and an Integral Representation for Appell k-Series F_(1,k)

“…Mubeen, et al [8] determined the contiguous function relations for -hypergeometric functions with one parameter corresponding to Gauss fifteen contiguous function relations for hypergeometric functions and also they obtained contiguous function relations for two parameters.…”