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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Duplication formulae involving Jacobi theta functions and Gosper's $ q$-trigonometric functions


Author: István Mező
Journal: Proc. Amer. Math. Soc. 141 (2013), 2401-2410
MSC (2010): Primary 33E05
Published electronically: March 26, 2013
MathSciNet review: 3043021
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Abstract: Using the $ q$-trigonometric definitions of Gosper, we devise a new $ q$-exponential function. Based on this concept, we derive a number of identities involving the Jacobi theta functions. These considerations lead to the answers to Gosper's ``mysteries''.


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Additional Information

István Mező
Affiliation: Department of Applied Mathematics and Probability Theory, Faculty of Informatics, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary
Email: mezo.istvan@inf.unideb.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11576-5
PII: S 0002-9939(2013)11576-5
Keywords: Jacobi theta functions, $q$-sine function, $q$-exponential function, duplication formulae
Received by editor(s): February 4, 2011
Received by editor(s) in revised form: October 17, 2011, and October 20, 2011
Published electronically: March 26, 2013
Additional Notes: This research was supported by OTKA grant No. K75566.
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.