Open Access
March 2017 Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu
Wenchang Chu
Proc. Japan Acad. Ser. A Math. Sci. 93(3): 13-15 (March 2017). DOI: 10.3792/pjaa.93.13

Abstract

By means of the telescoping method, we prove an infinite series identity with four free parameters. Its limiting case is utilized, with the help of the Pfaff transformation, not only to present a new proof for a ${_{2}}F_{1}$-series identity conjectured by Gosper (1977) and proved recently by Ebisu (2013), but also to establish an extension of the binomial series.

Citation

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Wenchang Chu. "Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu." Proc. Japan Acad. Ser. A Math. Sci. 93 (3) 13 - 15, March 2017. https://doi.org/10.3792/pjaa.93.13

Information

Published: March 2017
First available in Project Euclid: 2 March 2017

zbMATH: 1370.33007
Digital Object Identifier: 10.3792/pjaa.93.13

Subjects:
Primary: 33C20
Secondary: 05A19

Keywords: binomial series , Classical hypergeometric series , Pfaff transformation , telescoping method

Rights: Copyright © 2017 The Japan Academy

Vol.93 • No. 3 • March 2017
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