Parameter augmentation and the q-Gosper algorithm

• Autores: Yan-Ping Mu
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 43, Nº 12, 2008, págs. 874-882
• Idioma: inglés
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• Resumen

  • We develop a method for deriving new basic hypergeometric identities from old ones by parameter augmentation. The main idea is to introduce a new parameter and use the q-Gosper algorithm to find out a suitable form of the summand. By this method, we recover some classical formulas on basic hypergeometric series and find extensions of the Rogers�Fine identity and Ramanujan�s summation formula. Moreover, we derive an identity for a summation.