Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions

Abstract

Abstract In this paper, we assess an integral containing incomplete H-functions and utilize it to build up an expansion formula for the incomplete H-functions including the Bessel function. Next, we evaluate an integral containing incomplete H̅-functions and use it to develop an expansion formula for the incomplete H̅-functions including the Bessel function. The outcomes introduced in this paper are general in nature, and several particular cases can be acquired by giving specific values to the parameters engaged with the principle results. As particular cases, we derive expansions for the incomplete Meijer G ( Γ ) ${}^{(\Gamma )}G$ -function, Fox–Wright Ψ q ( Γ ) p ${}_{p}\Psi _{q}^{(\Gamma )}$ -function, and generalized hypergeometric Γ q p ${}_{p}\Gamma _{q}$ function.

Keywords

• Fox’s H-function
• Incomplete H-functions
• Incomplete H̅-functions
• Mellin–Barnes contour integral
• Bessel function