Proving some identities of gosper on q-trigonometric functions

Mohamed El Bachraoui; Mourad Ismail

doi:10.1090/proc/14084

Proving some identities of gosper on q-trigonometric functions

Mohamed El Bachraoui, Mourad Ismail

Department of Mathematical Sciences

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

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2009-2019
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	5
DOIs	https://doi.org/10.1090/proc/14084
Publication status	Published - May 2019

Keywords

Elliptic functions
Q-trigonometric functions
Theta function identities

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "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. ",

keywords = "Elliptic functions, Q-trigonometric functions, Theta function identities",

author = "{El Bachraoui}, Mohamed and Mourad Ismail",

note = "Funding Information: The author is grateful to the referee for valuable comments and interesting suggestions. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

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AB - 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.

KW - Elliptic functions

KW - Q-trigonometric functions

KW - Theta function identities

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Proving some identities of gosper on q-trigonometric functions

Abstract

Keywords

ASJC Scopus subject areas

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