On q-analogues for trigonometric identities

Sarah Abo Touk, Zina Al Houchan, Mohamed El Bachraoui

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)105-112
Number of pages8
JournalAnalysis (Germany)
Volume40
Issue number2
DOIs
Publication statusPublished - May 1 2020

Keywords

  • elliptic functions
  • theta function identities

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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