On q-analogues for trigonometric identities

Sarah Abo Touk; Zina Al Houchan; Mohamed El Bachraoui

doi:10.1515/anly-2018-0040

On q-analogues for trigonometric identities

Sarah Abo Touk, Zina Al Houchan, Mohamed El Bachraoui

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

In this paper we will give q-analogues for the Pythagorean trigonometric identity sin²z + cos²z = 1 in terms of Gosper's q-trigonometry. We shall also give new q-analogues for the duplicate trigonometric identity sin (x + y) = sin² x - sin². Moreover, we shall give a short proof for an identity of Gosper, which was also established by Mezo. The main argument of our proofs is the residue theorem applied to elliptic functions.

Original language	English
Pages (from-to)	105-112
Number of pages	8
Journal	Analysis (Germany)
Volume	40
Issue number	2
DOIs	https://doi.org/10.1515/anly-2018-0040
Publication status	Published - May 1 2020

Keywords

elliptic functions
theta function identities

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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author = "{Abo Touk}, Sarah and {Al Houchan}, Zina and {El Bachraoui}, Mohamed",

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AU - El Bachraoui, Mohamed

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N2 - In this paper we will give q-analogues for the Pythagorean trigonometric identity sin2z + cos2z = 1 in terms of Gosper's q-trigonometry. We shall also give new q-analogues for the duplicate trigonometric identity sin (x + y) = sin2 x - sin2. Moreover, we shall give a short proof for an identity of Gosper, which was also established by Mezo. The main argument of our proofs is the residue theorem applied to elliptic functions.

AB - In this paper we will give q-analogues for the Pythagorean trigonometric identity sin2z + cos2z = 1 in terms of Gosper's q-trigonometry. We shall also give new q-analogues for the duplicate trigonometric identity sin (x + y) = sin2 x - sin2. Moreover, we shall give a short proof for an identity of Gosper, which was also established by Mezo. The main argument of our proofs is the residue theorem applied to elliptic functions.

KW - elliptic functions

KW - theta function identities

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JO - Analysis (Germany)

JF - Analysis (Germany)

IS - 2

ER -

On q-analogues for trigonometric identities

Abstract

Keywords

ASJC Scopus subject areas

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