The q-WZ method for infinite series

• Autores: William Y. C. Chen, Ernest X.W. Xia
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 8, 2009, págs. 960-971
• Idioma: inglés
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• Resumen

  • 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 65 sum, the Ramanujan�s 1?1 sum and Bailey�s 6?6 sum.