De Sole, Kac: On integral representations of $q$-gamma and $q$-beta functions

De Sole, Alberto and Kac, Victor G.:
On integral representations of $q$-gamma and $q$-beta functions (Sulle rappresentazioni integrali delle funzioni $q$-gamma e $q$-beta)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 16 (2005), fasc. n.1, p. 11-29, (English)
pdf (307 Kb), djvu (216 Kb). | MR2225920 | Zbl 1225.33017

Sunto

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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Referenza completa

Sunto

Referenze Bibliografiche