Proving some identities of gosper on q-trigonometric functions

Mohamed El Bachraoui, Mourad Ismail

Research output: Contribution to journalArticlepeer-review

4 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 languageEnglish
Pages (from-to)2009-2019
Number of pages11
JournalProceedings of the American Mathematical Society
Volume147
Issue number5
DOIs
Publication statusPublished - May 2019

Keywords

  • Elliptic functions
  • Q-trigonometric functions
  • Theta function identities

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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