On the Gosper’s q-constant Πq

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Gosper introduced the functions sinqz and cosqz as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn (n ∈ N). Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.

Original languageEnglish
Pages (from-to)1755-1764
Number of pages10
JournalActa Mathematica Sinica, English Series
Issue number11
Publication statusPublished - Nov 1 2018


  • 11F11
  • 11F12
  • 33E05
  • elliptic functions
  • q-trigonometric functions
  • theta function identities

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'On the Gosper’s q-constant Πq'. Together they form a unique fingerprint.

Cite this