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Terminating balanced $ _4\phi_3$-series with two integer parameters

Authors: Nadia N. Li and Wenchang Chu
Journal: Proc. Amer. Math. Soc. 145 (2017), 4371-4383
MSC (2010): Primary 33D15; Secondary 05A30
Published electronically: May 24, 2017
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Abstract: The linearization method is employed to investigate a class of terminating almost-balanced $ _4\phi _3$-series perturbed by two extra integer parameters. Three analytical expressions are established that contain several closed formulae as special cases. By means of a combination with Watson's transformation, these formulae are utilized, in turn, to evaluate a class of terminating well-poised $ _8\phi _7$-series.

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Nadia N. Li
Affiliation: Department of Mathematics, Zhoukou Normal University, Zhoukou 466000, People’s Republic of China

Wenchang Chu
Affiliation: Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce–Arnesano P. O. Box 193, 73100 Lecce, Italy

Keywords: Basic hypergeometric series, linearization method, well--poised series, balanced series, the $q$-Pfaff--Saalsch\"utz theorem, Watson's transformation
Received by editor(s): October 31, 2016
Published electronically: May 24, 2017
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2017 American Mathematical Society

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