Proofs for two q-trigonometric identities of Gosper

Sarah Abo Touk; Zina Al Houchan; Mohamed El Bachraoui

doi:10.1016/j.jmaa.2017.07.030

Proofs for two q-trigonometric identities of Gosper

Sarah Abo Touk
, Zina Al Houchan
, Mohamed El Bachraoui

Department of Mathematical Sciences

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

10 Citations (Scopus)

Abstract

In 2001, Gosper introduced q-analogues for the functions sin⁡z and cos⁡z and stated without proofs many identities involving these q-analogues. Gosper asked whether his formulas are true. In this paper, we shall use the theory of elliptic functions to confirm two of Gosper's identities. Moreover, we shall give two consequences of these identities.

Original language	English
Pages (from-to)	662-670
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	456
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2017.07.030
Publication status	Published - Dec 1 2017

Keywords

Elliptic functions
Theta function identities
q-Trigonometric functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2017.07.030

Cite this

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abstract = "In 2001, Gosper introduced q-analogues for the functions sin⁡z and cos⁡z and stated without proofs many identities involving these q-analogues. Gosper asked whether his formulas are true. In this paper, we shall use the theory of elliptic functions to confirm two of Gosper's identities. Moreover, we shall give two consequences of these identities.",

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AU - El Bachraoui, Mohamed

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N2 - In 2001, Gosper introduced q-analogues for the functions sin⁡z and cos⁡z and stated without proofs many identities involving these q-analogues. Gosper asked whether his formulas are true. In this paper, we shall use the theory of elliptic functions to confirm two of Gosper's identities. Moreover, we shall give two consequences of these identities.

AB - In 2001, Gosper introduced q-analogues for the functions sin⁡z and cos⁡z and stated without proofs many identities involving these q-analogues. Gosper asked whether his formulas are true. In this paper, we shall use the theory of elliptic functions to confirm two of Gosper's identities. Moreover, we shall give two consequences of these identities.

KW - Elliptic functions

KW - Theta function identities

KW - q-Trigonometric functions

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Proofs for two q-trigonometric identities of Gosper

Abstract

Keywords

ASJC Scopus subject areas

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