On Certain Integrals Related to Saran’s Hypergeometric Function <i>F_K</i>

Abstract

In the present paper, we establish two Erdélyi-type integrals for Saran’s hypergeometric function FK, which has applications in specific branches of applied physics and statistics (see below). We employ methods based on the k-dimensional fractional integration by parts to obtain our main integral identities. The first integral generalizes Koschmieder’s result and the second integral extends one of Erdélyi’s classical hypergeometric integral. Some useful special cases and important remarks are also discussed.

Keywords

• Erdélyi-type integral
• fractional integration by parts
• Saran’s function