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.
Highlights
Motivation and ObjectivesOne of the triple hypergeometric functions due to Saran ([1] p. 294, Equation (2.4); see [2]) is the FK function which is defined by Related to Saran’s Hypergeometric
The aim of the present paper is to obtain further new results related to the work on Erdélyi-type integrals for the FK function [2]
Hypergeometric functions of several variables have vastly been studied; see, for example, Refs. [9,23–26]. Due to their importance in the theory and applications, it is always useful and interesting to find new Erdélyi-type integrals associated with such classes of hypergeometric functions
Summary
One of the triple hypergeometric functions due to Saran ([1] p. 294, Equation (2.4); see [2]) is the FK function which is defined by Related to Saran’s Hypergeometric. The aim of the present paper is to obtain further new results related to the work on Erdélyi-type integrals for the FK function [2]. It was used in solving a certain Abel-type integral equation involving the Appell hypergeometric function F3 in the kernel [22]. Due to their importance in the theory and applications, it is always useful and interesting to find new Erdélyi-type integrals associated with such classes of hypergeometric functions. Sharma and Manocha’s Formula (4) is an interesting result that depicts an important fact that the Saran’s function FM has the Erdélyi-type integral relation. We show, by specializing a very general type of integral identity, that an integral representation of the Erdélyi-type similar to the result (4) holds for the FK function defined above by (1)
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