The Saalschütz chain reactions and bilateral basic hypergeometric series

By iterating recursively the q-Saalschütz summation formula, we introduce the Saalschütz chain reactions. A general series transform, which expresses a nonterminating bilateral series in terms of a finite multiple unilateral sum, will be established. As applications we derive, by means of Bailey’s 6...

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Bibliographic Details
Published in:Constructive approximation Vol. 18; no. 4; pp. 579 - 597
Main Author: Chu, Wenchang
Format: Journal Article
Language:English
Published: New York, NY Springer 01.01.2002
Springer Nature B.V
Subjects:
Classical combinatorial problems
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Mathematical analysis
Mathematics
Sciences and techniques of general use
Series (mathematics)
Special functions
Chain reaction
Hypergeometric series
Bilateral hypergeometric series
Basic hypergeometric series
Saalschtz chain reaction
Summation
Convergence
ISSN:0176-4276, 1432-0940
Online Access:Get full text
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Summary:By iterating recursively the q-Saalschütz summation formula, we introduce the Saalschütz chain reactions. A general series transform, which expresses a nonterminating bilateral series in terms of a finite multiple unilateral sum, will be established. As applications we derive, by means of Bailey’s 6ψ6 -series identity, several bilateral transformations including one due to Milne [12]. These transformations further yield a number of closed formulas of very well-poised bilateral basic hypergeometric series; which are closely related to the identities obtained by Minton [13], Karlsson [11], Gasper [8], and Chu [5], [6], [7] through the partial fraction method and divided differences.
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ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-001-0026-4