On integral representations of q-gamma and q-beta functions
De Sole, Alberto ; Kac, Victor G.
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 16 (2005), p. 11-29 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

Publié le : 2005-03-01
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     author = {Alberto De Sole and Victor G. Kac},
     title = {On integral representations of $q$-gamma and $q$-beta functions},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {16},
     year = {2005},
     pages = {11-29},
     zbl = {1225.33017},
     mrnumber = {2225920},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2005_9_16_1_11_0}
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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. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 16 (2005) pp. 11-29. http://gdmltest.u-ga.fr/item/RLIN_2005_9_16_1_11_0/

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