On integral representations of $q$-gamma and $q$-beta functions
210 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/64df219e585ee624a74af0548d381461c782a0fd
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In Applied Mathematics
- Ferhan Merdivenci Atici
- Paul W. Eloe
- Christopher S. Goodrich
- Carlos Lizama
- Thabet Abdeljawad
- Rui A. C. Ferreira
- Meltem Uyanik
- Dumitru Băleanu
Citations in the corpus
- Fractional q-Calculus on a time scale (2007, background): “Eloe [10], McAnally ([22], [23]), Ernst [12], and Koornwinder [20], [21] and books by Andrews, Askey, Verma [6] and Carlson [9] for current and excellent accounts of q-special functions.”