On several new contiguous function relations for k-hypergeometric function with two parameters
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Very recently, Mubeen, et al.~\cite{5} have obtained fifteen contiguous function relations for $k$-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for $k$-hypergeometric functions with two parameters. Obviously, for $k\rightarrow 1$ we recover the results obtained by Cho, et al.~\cite{2} and Rakha, et al.~\cite{7}.
Abstract
Very recently, Mubeen, et al.~\cite{5} have obtained fifteen contiguous function relations for $k$-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for $k$-hypergeometric functions with two parameters. Obviously, for $k\rightarrow 1$ we recover the results obtained by Cho, et al.~\cite{2} and Rakha, et al.~\cite{7}.
참고문헌 (8)
- G. E. Andrews, "Special Functions" (1999), Cambridge University Press
- Y. J. Cho, "A note on contiguous function relations", East Asian Math. J, 15(1), pp.29~38 (1999)
- C. Diaz, "On hypergeometric functions and Pochhammer k-symbol", Divulg. Math, 15(2), pp.179~192 (2007)
- C. F. Gauss, "Disquisitiones generales circa seriem infinitam", Werke, 3, pp.123~162 (1876)
- M. Mansour, "Determining the k-generalized gamma function (x) by functional equa-tions", Int. J. Contemp. Math. Sci, 4(21-24), pp.1037~1042 (2009)
- S. Mubeen, "Contiguous function relations for k-Hypergeometric Functions", ISRN Math. Anal, 2014 (2014)
- E. D. Rainvile, "Special Functions" (1960), Macmillan Company
- M. A. Rakha, "On some new contiguous function relations for the Gauss hypergeometric Function with applications", Computers Math. Appl, 61, pp.620~629 (2011)