The q -WZ method for infinite series

Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q -shifted factorials can be incorporated into the implementation of the q -Zeilberger algorithm in the approach of Chen, Hou and Mu to prove nonterminating basic hypergeometric series identities. Thi...

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Vydáno v:	Journal of symbolic computation Ročník 44; číslo 8; s. 960 - 971
Hlavní autoři:	Chen, William Y.C., Xia, Ernest X.W.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Ltd 01.08.2009
Témata:	Basic hypergeometric series The [formula omitted]-Gosper algorithm The [formula omitted]-WZ method The [formula omitted]-Zeilberger algorithm Basic hypergeometric series The q -Gosper algorithm The q -WZ method The q -Zeilberger algorithm
ISSN:	0747-7171, 1095-855X
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Popis
Shrnutí:	Motivated by the telescoping proofs of two identities of Andrews and Warnaar, we find that infinite q -shifted factorials can be incorporated into the implementation of the q -Zeilberger algorithm in the approach of Chen, Hou and Mu to prove nonterminating basic hypergeometric series identities. This observation enables us to extend the q -WZ method to identities on infinite series. We give the q -WZ pairs for some classical identities such as the q -Gauss sum, the 6 ϕ 5 sum, the Ramanujan’s 1 ψ 1 sum and Bailey’s 6 ψ 6 sum.
ISSN:	0747-7171 1095-855X
DOI:	10.1016/j.jsc.2008.11.005