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.
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