Duplication formulae involving Jacobi theta functions and Gosper's trigonometric functions
Author:
István Mező
Journal:
Proc. Amer. Math. Soc. 141 (2013), 24012410
MSC (2010):
Primary 33E05
Published electronically:
March 26, 2013
MathSciNet review:
3043021
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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, H4010, Debrecen, Hungary
Email:
mezo.istvan@inf.unideb.hu
DOI:
http://dx.doi.org/10.1090/S000299392013115765
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.
