Showing papers on "q-gamma function published in 2005"
1 Jan 2005
TL;DR: In this article, q-integral representations of the q-gamma and q-beta functions are studied and a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and Ramanujan's formula for the bilateral hypergeometric series is given.
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
175 citations
1 Jan 2005
TL;DR: In this paper, three basic properties of logarithmically N-alternating monotonic functions are established and the monotonicity results of some functions involving the gamma and q-gamma functions, which are obtained by W. E. Clark and M. H. Ismail.
Abstract: In the paper, three basic properties of the logarithmically N-alternating
monotonic functions are established and the monotonicity results
of some functions involving the gamma and q-gamma functions, which are obtained
in [W. E. Clark and M. E. H. Ismail, Inequalities involving gamma and
psi functions, Anal. Appl. (Singap.) 1 (2003), no. 1, 129–140.], are generalized
to the logarithmically N-alternating monotonicity.
42 citations
TL;DR: In this paper, it was shown that various functions related to the logarithms of the canonical products Pρ(z) = Πn=1∞ (1 + Z/nρ), ρ > 1 and Q(z), q ∈ (0, 1) are Pick functions.
7 citations
1 Jan 2005
TL;DR: In this article, the authors prove properties of completely monotonic functions and apply them to obtain new results on gamma and q-gamma functions, and apply these properties to other functions as well.
Abstract: We prove some properties of completely monotonic functions and apply them to obtain
new results on gamma and q-gamma functions.
2 citations
TL;DR: In this article, the Smarandache cyclic de-terminants and bisymmetric determinants were solved, and some conjectures about the latter were also solved.
Abstract: In this paper we solve some conjectures concerned the Smarandache cyclic de-terminants and the Smarandache bisymmetric determinants
28 Sep 2005
TL;DR: In this paper, an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic were given. And they were shown to give an infinitely divisible probability distribution for specific combinations of the gamma and q-gamma functions.
Abstract: We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.