Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2012; 27(1): 107-116

Printed March 1, 2012

https://doi.org/10.4134/CKMS.2012.27.1.107

Copyright © The Korean Mathematical Society.

Certain decomposition formulas of generalized hypergeometric functions ${}_pF_q$ and some formulas of an analytic continuation of the Clausen function ${}_3F_2$

Junesang Choi and Anvar Hasanov

Dongguk University, Dongguk University

Abstract

Here, by using the symbolical method introduced by Burchnall and Chaundy, we aim at constructing certain expansion formulas for the generalized hypergeometric function ${}_pF_q$. In addition, using our expansion formulas for ${}_pF_q$, we present formulas of an analytic continuation of the Clausen hypergeometric function ${}_3F_2$, which are much simpler than an earlier known result. We also give some integral representations for ${}_3F_2$.

Keywords: generalized hypergeometric series, inverse pairs of symbolic, decomposition formulas, Gauss function, Clausen function, formulas of analytic continuations

MSC numbers: Primary 33C20; Secondary 44A45