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

Alberto De Sole·Victor Kac
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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.

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Alberto De Sole, Victor Kac. 2003-02-04. On integral representations of q-gamma and q-beta functions. https://arxiv.org/abs/math/0302032

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