Some New Formulas for Horn's Hypergeometric Functions H_1, H_2, H_3, H_4, H_5, H_6, and H_7

Ayman Shehata, Shimaa I. Moustafa

Abstract

The aim of this work is to demonstrate various an interesting recursion formulas, differential recursion formulas, differential operators, integral operators, integration formulas, and generating relations for each of Horn's hypergeometric functions $\mathbf{H}_{1}$, $\mathbf{H}_{2}$, $\mathbf{H}_{3}$, $\mathbf{H}_{4}$, $\mathbf{H}_{5}$, $\mathbf{H}_{6}$ and $\mathbf{H}_{7}$ by the contiguous relations of Horn's hypergeometric series. Some interesting special cases of our main results are also constructed.