Telescopic approach to a formula of [sub.2][F.sub.1]-series by Gosper and Ebisu

Telescopic approach to a formula of [sub.2][F.sub.1]-series by Gosper and Ebisu

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 [sub.2][F.sub.1]-series identity conjectured by Gosper (1977) and proved recently by Ebi...

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Veröffentlicht in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2017-03, Vol.93A (3), p.13-15
1. Verfasser: Chu, Wenchang
Format: Artikel
Sprache:eng
Schlagworte:
Binomials
Constraining
Formulas (mathematics)
Infinite series
Mathematical analysis
Mathematical research
Mathematics
Series (Mathematics)
Telescoping
Transformations (Mathematics)
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Zusammenfassung: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 [sub.2][F.sub.1]-series identity conjectured by Gosper (1977) and proved recently by Ebisu (2013), but also to establish an extension of the binomial series. Key words: Classical hypergeometric series; binomial series; telescoping method; Pfaff transformation.
ISSN:0386-2194
DOI:10.3792/pjaa.93.13