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.
Junesang Choi and Anvar Hasanov
Dongguk University, Dongguk University
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
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