A study of the k-Horn’s hypergeometric function H9,k

Abstract

In this paper, we introduce the k-Horn’s hypergeometric function H9,k and we investigate its limit formulas, integral representations, differentiation formulas, infinite sums, recursion formulas, the Laplace, Mellin, fractional Fourier, double Laplace and double Mellin transforms for the k-Horn’s hypergeometric function H9,k . Finally, we discuss the fractional integration and the k-fractional differentiation.