Proving some identities of Gosper on 𝑞-trigonometric functions

El Bachraoui, Mohamed

doi:10.1090/proc/14084

Proving some identities of Gosper on $q$-trigonometric functions
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by Mohamed El Bachraoui PDF

Proc. Amer. Math. Soc. 147 (2019), 2009-2019 Request permission

Abstract:

Gosper introduced the functions $\sin _q z$ and $\cos _q z$ as $q$-analogues for the trigonometric functions $\sin z$ and $\cos z$ respectively. He stated but did not prove a variety of identities involving these two $q$-trigonometric functions. In this paper, we shall use the theory of elliptic functions to prove three formulas from the list of Gosper on the functions $\sin _q z$ and $\cos _q z$.

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