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

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
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     title = {On integral representations of $q$-gamma and $q$-beta functions},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {11--29},
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     number = {1},
     year = {2005},
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     mrnumber = {MR2225920},
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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/