English

On integral representations of q-gamma and q-beta functions

Quantum Algebra 2015-12-18 v1

Abstract

We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and of Ramanujan's formula for the bilateral hypergeometric series.

Keywords

Cite

@article{arxiv.math/0302032,
  title  = {On integral representations of q-gamma and q-beta functions},
  author = {Alberto De Sole and Victor Kac},
  journal= {arXiv preprint arXiv:math/0302032},
  year   = {2015}
}

Comments

16 pages

R2 v1 2026-07-22T16:51:42.017Z