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
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
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