Analytical formulae for extended ₃𝐹₂-series of Watson–Whipple–Dixon with two extra integer parameters

Chu, Wenchang

doi:10.1090/S0025-5718-2011-02512-3

Analytical formulae for extended $_3F_2$-series of Watson–Whipple–Dixon with two extra integer parameters
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by Wenchang Chu;

Math. Comp. 81 (2012), 467-479

DOI: https://doi.org/10.1090/S0025-5718-2011-02512-3

Published electronically: June 30, 2011

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Abstract:

By combining the linearization method with Dougall’s sum for well–poised $_5F_4$-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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