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Analytical formulae for extended $_3F_2$-series of Watson鈥揥hipple鈥揇ixon with two extra integer parameters


Author: Wenchang Chu
Journal: Math. Comp. 81 (2012), 467-479
MSC (2010): Primary 33C20; Secondary 05A10
DOI: https://doi.org/10.1090/S0025-5718-2011-02512-3
Published electronically: June 30, 2011
MathSciNet review: 2833504
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Abstract: By combining the linearization method with Dougall鈥檚 sum for well鈥損oised $_5F_4$-series, we investigate the generalized Watson series with two extra integer parameters. Four analytical formulae are established, which can also be used to evaluate the extended Whipple and Dixon series via the Thomae transformation. Twelve concrete formulae are presented as exemplification.


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Additional Information

Wenchang Chu
Affiliation: Hangzhou Normal University, Institute of Combinatorial Mathematics, Hangzhou 310036, People鈥檚 Republic of China
Address at time of publication: Dipartimento di Matematica, Universit脿 del Salento, Lecce鈥揂rnesano, P.O. Box 193, Lecce 73100, Italy
MR Author ID: 213991
Email: chu.wenchang@unisalento.it

Keywords: Classical hypergeometric series, Dixon鈥檚 theorem, Watson鈥檚 formula, Whipple鈥檚 formula, The Thomae transformation, Dougall鈥檚 theorem for well鈥損oised series
Received by editor(s): October 8, 2010
Received by editor(s) in revised form: November 30, 2010, and December 24, 2010
Published electronically: June 30, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.