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Axioms 2012, 1(3), 365-371; doi:10.3390/axioms1030365

Article

New Curious Bilateral q-Series Identities

Frédéric Jouhet ^1,*  and Michael J. Schlosser ²

¹ Institut Camille Jordan, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France ² Fakultät für Mathematik der Universität Wien, Nordbergstraße 15, A-1090 Wien, Austria

* Author to whom correspondence should be addressed.

Received: 17 September 2012; in revised form: 9 October 2012 / Accepted: 17 October 2012 / Published: 31 October 2012

(This article belongs to the Special Issue q-Series and Related Topics in Special Functions and Analytic Number Theory)

Download PDF Full-Text [144 KB, uploaded 31 October 2012 08:20 CET]

Abstract: By applying a classical method, already employed by Cauchy, to a terminating curious summation by one of the authors, a new curious bilateral q-series identity is derived. We also apply the same method to a quadratic summation by Gessel and Stanton, and to a cubic summation by Gasper, respectively, to derive a bilateral quadratic and a bilateral cubic summation formula.

Keywords: bilateral basic hypergeometric series; q-series; curious summations

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