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

Author:
István Mező

Journal:
Proc. Amer. Math. Soc. **141** (2013), 2401-2410

MSC (2010):
Primary 33E05

DOI:
https://doi.org/10.1090/S0002-9939-2013-11576-5

Published electronically:
March 26, 2013

MathSciNet review:
3043021

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Abstract | References | Similar Articles | Additional Information

Abstract: Using the -trigonometric definitions of Gosper, we devise a new -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:
https://doi.org/10.1090/S0002-9939-2013-11576-5

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.