We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. 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.
On the integral representation of the q-gamma and the q-beta functions / DE SOLE, Alberto; Kac, V.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1720-0768. - STAMPA. - 16:9(2005), pp. 11-29.
On the integral representation of the q-gamma and the q-beta functions
DE SOLE, ALBERTO;
2005
Abstract
We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. 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.File allegati a questo prodotto
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