Proving some identities of Gosper on q-trigonometric functions

2018/01/11 by Bachraoui, Mohamed El
#11F11 #11F12 #33E05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.03654

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.

Related

• Proofs for certain conjectures of Gosper on q-trigonometric identities
• On certain q-trigonometric identities
• Some new sums of q-trigonometric and related functions through a theta product of Jacobi
• Extensions of two q-Gosper identities with an extra integer parameter
• Proofs for certain Pi_q-conjectures of Gosper