Proofs for certain conjectures of Gosper on q-trigonometric identities
Classical Analysis and ODEs
2021-05-10 v2 Number Theory
Abstract
Applying the theory of elliptic functions we establish two Jacobi theta function identities. From these identities we confirm two q-trigonometric identities conjectured by Gosper. As an application, we give a new and simple proof of a Pi_{q}-identity of Gosper.
Keywords
Cite
@article{arxiv.2010.05011,
title = {Proofs for certain conjectures of Gosper on q-trigonometric identities},
author = {Bing He},
journal= {arXiv preprint arXiv:2010.05011},
year = {2021}
}
Comments
This article is withdrawn because one of the main results (Theorem 1.1) is a special case of Weierstrass' addition formula (also called the Riemann relation)