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Confirming a $ q$-trigonometric conjecture of Gosper


Author: Mohamed El Bachraoui
Journal: Proc. Amer. Math. Soc. 146 (2018), 1619-1625
MSC (2010): Primary 33E05, 11F11, 11F12
DOI: https://doi.org/10.1090/proc/13830
Published electronically: November 7, 2017
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Abstract: We shall confirm a conjecture of Gosper on the $ q$-analogue of the function $ \mathrm {cos}(2z)$ and we shall give a short proof for his other related identity on the $ q$-analogue of $ \mathrm {sin}(2z)$ which was recently proved by Mező.


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Additional Information

Mohamed El Bachraoui
Affiliation: Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al-Ain, United Arab Emirates
Email: melbachraoui@uaeu.ac.ae

DOI: https://doi.org/10.1090/proc/13830
Keywords: $q$-trigonometric functions; elliptic functions, theta function identities
Received by editor(s): February 2, 2017
Received by editor(s) in revised form: May 18, 2017
Published electronically: November 7, 2017
Communicated by: Mourad Ismail
Article copyright: © Copyright 2017 American Mathematical Society

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