Duplication formulae involving Jacobi theta functions and Gosper’s $q$-trigonometric functions
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- by István Mező PDF
- Proc. Amer. Math. Soc. 141 (2013), 2401-2410 Request permission
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”.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2401-2410
- MSC (2010): Primary 33E05
- DOI: https://doi.org/10.1090/S0002-9939-2013-11576-5
- MathSciNet review: 3043021