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Terminating $ {}_2F_1(4)$-series perturbed by two integer parameters


Author: Wenchang Chu
Journal: Proc. Amer. Math. Soc. 145 (2017), 1031-1040
MSC (2010): Primary 05A19; Secondary 33C20
DOI: https://doi.org/10.1090/proc/13293
Published electronically: September 15, 2016
MathSciNet review: 3589303
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Abstract: By means of generating functions and the linearization method, we establish analytical formulae for a class of terminating $ _2F_1(4)$-series perturbed by two integer parameters. Under the Pfaff transformation, these formulae confirm, unexpectedly, a conjecture about evaluation of the $ _2F_1(-3)$-series made by Apagodu and Zeilberger (2008).


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Additional Information

Wenchang Chu
Affiliation: Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce–Arnesano P.O. Box 193, 73100 Lecce, Italia
Email: chu.wenchang@unisalento.it

DOI: https://doi.org/10.1090/proc/13293
Keywords: Terminating hypergeometric series, generating function, linearization method, Chu--Vandermonde formula, Kummer's summation theorem, Pfaff transformation
Received by editor(s): May 6, 2016
Received by editor(s) in revised form: May 15, 2016
Published electronically: September 15, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society