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 Certain decomposition formulas of generalized hypergeometric functions ${}_pF_q$ and some formulas of an analytic continuation of the Clausen function ${}_3F_2$ Commun. Korean Math. Soc. 2012 Vol. 27, No. 1, 107-116 https://doi.org/10.4134/CKMS.2012.27.1.107Printed March 1, 2012 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 Downloads: Full-text PDF

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