Proving some identities of Gosper on $q$-trigonometric functions

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 ${\cos }_{q}z$.

Accepted in Proc. Amer. Math. Soc

Cited by in corpus (1)

• Proofs for certain Pi_{q}-conjectures of Gosper