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 |
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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. |
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ISSN: | 0196-8858 1090-2074 |
DOI: | 10.1016/j.aam.2009.02.001 |