Solving some q-trigonometric conjectures of Gosper

Mohamed El Bachraoui

doi:10.1016/j.jmaa.2017.12.016

Solving some q-trigonometric conjectures of Gosper

Mohamed El Bachraoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Gosper in 2001 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, many identities involving the functions sin_q⁡z and cos_q⁡z along with some other related functions and constants. In this note we shall provide proofs for some of these identities by means of the classical theory of elliptic functions.

Original language	English
Pages (from-to)	610-617
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	460
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2017.12.016
Publication status	Published - Apr 15 2018

Keywords

Elliptic functions
Theta function identities
q-trigonometric functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2017.12.016

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AB - Gosper in 2001 introduced the functions sinq⁡z and cosq⁡z as q-analogues for the trigonometric functions sin⁡z and cos⁡z respectively. He stated, but did not prove, many identities involving the functions sinq⁡z and cosq⁡z along with some other related functions and constants. In this note we shall provide proofs for some of these identities by means of the classical theory of elliptic functions.

KW - Elliptic functions

KW - Theta function identities

KW - q-trigonometric functions

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Solving some q-trigonometric conjectures of Gosper

Abstract

Keywords

ASJC Scopus subject areas

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