Some Summation Formulae for Nonterminating Basic Hypergeometric Series

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1985 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 16, pages 647-655 (issn: 0036-1410, eissn: 1095-7154,

Copyright policy )

Authors: Verma, A.; Jain, V. K.;

doi: 10.1137/0516048

Some Summation Formulae for Nonterminating Basic Hypergeometric Series

- Summary
- Subjects
- Metrics

Abstract

Andrews found basic hypergeometric extensions of the Watson and Whipple \({}_ 3F_ 2\) sums in the terminating cases. His series were balanced \({}_ 4\phi_ 3's\). By Watson's transformation these can be written as very well poised \({}_ 8\phi_ 7's\). The authors obtain nonterminating extensions of these \({}_ 3F_ 2\) sums as very well poised \({}_ 8\phi_ 7's\). They also obtain basic hypergeometric extensions of two Cayley-Orr type formulas.

Keywords

Cayley-Orr type formulas, Basic hypergeometric functions in one variable, \({}_r\phi_s\), basic hypergeometric series

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	7
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average