## 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 language | English |
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Pages (from-to) | 2009-2019 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2019 |

## Keywords

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

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics