Extended Horn’s hypergeometric function $H_{11}$

Abstract

In this paper we introduce an extension of the Horn’s hypergeometric function $H_{11}$. Furthermore, we investigate the limit formulas, integral representations, differentiation formulas, infinite sums, recursion formulas, Laplace, Mellin and fractional Fourier transforms for the extended Horn’s hypergeometric function $H_{11}$. Finally, we discuss double Laplace and double Mellin transforms of this function.