Geodesic
On integral representations of $q$-gamma and $q$-beta functions
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 1, pp. 11-29.

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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.
Studiamo la rappresentazione $q$-integrale delle funzioni $q$-gamma e $q$-beta. Questo studio svela una $q$-costante molto interessante. Come applicazione di queste rappresentazioni integrali, otteniamo una semlice dimostrazione concettuale di una famiglia di identità per il prodotto triplo di Jacobi, che include l'identità di Jacobi, e della formula di Ramanujan per le serie ipergeometriche bilaterali. 
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De Sole, Alberto; Kac, Victor G. On integral representations of $q$-gamma and $q$-beta functions. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 16 (2005) no. 1, pp. 11-29. http://geodesic.mathdoc.fr/item/RLIN_2005_9_16_1_a1/

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