Some new results for Horn's hypergeometric functions Γ 1 and Γ 2

Abstract

The object of the present work is to deduce several important developments in various recursion relations, relevant differential recursion formulas, infinite summation formulas, integral representations, and integral operators for Horn's hypergeometric functions Γ 1 and Γ 2 .

Some Formulas for Horn’s Hypergeometric Function G B of Three Variables

“…Our paper is generally based on the extension of Horn's hypergeometric functions of two variables. A few specializations relevant to the present discussion have also been derived from results of papers [33][34][35]38]. We focused on the generalization of the Horn's function G B of three variables and presented some partial differential equations, differential recursion formulas, series representations, integral representations and infinite summations.…”

“…In our present work, we establish some new differentiation formulas, differential equations, recursion relations, differential recursion relations, confluence formulas, series representations, integration formulas, and infinite summations for the Horn hypergeometric function G B of three variables by using the technique of Ibrahim [25], Ibrahim and Rakha [26], Rakha and Ibrahim [27], Rakha et al [28], Kim et al [29] and Brychkov and Savischenko [30][31][32]. Pathan et al [33], and Shehata and Shimaa [34,35] found 7 and 11 hypergeometric series in two variables of order two. We shall derive these G B series from our viewpoint.…”