# zbMATH — the first resource for mathematics

On integral representations of $$q$$-gamma and $$q$$-beta functions. (English) Zbl 1225.33017
Summary: We study $$q$$-integral representations of the $$q$$-gamma and the $$q$$-beta functions. 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.

##### MSC:
 33D05 $$q$$-gamma functions, $$q$$-beta functions and integrals
##### Keywords:
$$q$$-calculus; $$q$$-gamma function; $$q$$-beta function
Full Text: