Proofs for two q-trigonometric identities of Gosper

Sarah Abo Touk, Zina Al Houchan, Mohamed El Bachraoui

Research output: Contribution to journalArticlepeer-review

8 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 languageEnglish
Pages (from-to)662-670
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume456
Issue number1
DOIs
Publication statusPublished - Dec 1 2017

Keywords

  • Elliptic functions
  • Theta function identities
  • q-Trigonometric functions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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