On integral representations of -gamma and -beta functions
Alberto De Sole; Victor G. Kac
- Volume: 16, Issue: 1, page 11-29
- ISSN: 1120-6330
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topDe Sole, Alberto, and 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 16.1 (2005): 11-29. <http://eudml.org/doc/252391>.
@article{DeSole2005,
abstract = {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.},
author = {De Sole, Alberto, Kac, Victor G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {$q$
q
-calculus; $q$
q
-gamma function; $q$
q
-beta function; -calculus; -gamma function; -beta function},
language = {eng},
month = {3},
number = {1},
pages = {11-29},
publisher = {Accademia Nazionale dei Lincei},
title = {On integral representations of $q$-gamma and $q$-beta functions},
url = {http://eudml.org/doc/252391},
volume = {16},
year = {2005},
}
TY - JOUR
AU - De Sole, Alberto
AU - Kac, Victor G.
TI - On integral representations of $q$-gamma and $q$-beta functions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/3//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 1
SP - 11
EP - 29
AB - 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.
LA - eng
KW - $q$
q
-calculus; $q$
q
-gamma function; $q$
q
-beta function; -calculus; -gamma function; -beta function
UR - http://eudml.org/doc/252391
ER -
References
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- THOMAE, J., Beitrage zur Theorie der durch die Heinesche Reihe. J. reine angew. Math., 70, 1869, 258-281. JFM02.0122.04
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