English

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

Number Theory 2018-01-12 v1

Abstract

Gosper introduced the functions sinqz\sin_q z and cosqz\cos_q z as qq-analogues for the trigonometric functions sinz\sin z and cosz\cos z respectively. He stated but did not prove a variety of identities involving these two qq-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 sinqz\sin_q z and cosqz\cos_q z.

Keywords

Cite

@article{arxiv.1801.03654,
  title  = {Proving some identities of Gosper on $q$-trigonometric functions},
  author = {Mohamed El Bachraoui},
  journal= {arXiv preprint arXiv:1801.03654},
  year   = {2018}
}

Comments

Accepted in Proc. Amer. Math. Soc