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CERTAIN DECOMPOSITION FORMULAS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS pFq AND SOME FORMULAS OF AN ANALYTIC CONTINUATION OF THE CLAUSEN FUNCTION 3F2

Choi, June-Sang;Hasanov, Anvar

  • Received : 2010.07.27
  • Published : 2012.01.31

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

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Cited by

  1. DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY vol.29, pp.1, 2014, https://doi.org/10.4134/CKMS.2014.29.1.097