On certain results related to the hypergeometric function FK

Motivated by some recent applications of a certain triple series hypergeometric function in the areas of physics and statistics, we investigate further Saran's work (e.g., [Acta Math. 93 (1955), 293-312]) related to this useful hypergeometric function FK. Its analytic continuation and asymptotics are obtained by establishing a new single contour integral representation. With the help of the fractional integration by parts, we prove a new integral identity and discuss in detail its various special cases and their relationship with Koschmieder's work [Acta Math. 79 (1947), 241-254]. Several consequences and special cases of the results presented in this paper are also mentioned. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

Motivated by recent applications in physics and statistics, this study further investigates Saran's work on the hypergeometric function FK. The analytic continuation and asymptotics of FK are obtained through a new single contour integral representation, and a new integral identity is proved using fractional integration by parts. Various special cases and their relationship with Koschmieder's work are discussed in detail.