Some implications of the WP-Bailey tree

We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some additional new transformations for basic hypergeometric series. Finally, we...

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Veröffentlicht in:Advances in applied mathematics 2009-08, Vol.43 (2), p.162-175
Hauptverfasser: Mc Laughlin, James, Zimmer, Peter
Format: Artikel
Sprache:eng
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Zusammenfassung:We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new WP-Bailey pairs, and use them to derive some additional new transformations for basic hypergeometric series. Finally, we briefly consider the implications of WP-Bailey pairs ( α n ( a , k ) , β n ( a , k ) ) , in which α n ( a , k ) is independent of k, for generalizations of identities of the Rogers–Ramanujan type.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2009.02.001