Some inequalities for the \(q,k\)-Gamma and Beta functions
Downloads
DOI:
https://doi.org/10.26637/mjm201/008Abstract
Using q-integral inequalities we establish some new inequalities for the \(q-k\) Gamma, Beta and Psi functions.
Keywords:
\(q,k\)-Gamma, \(q,k\)-Beta, \(q\)-integral inequalitiesMathematics Subject Classification:
33D05, 33D60, 41A17- Pages: 61-71
- Date Published: 01-01-2014
- Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)
R. Diaz, C. Teruel, q,k-Generalized Gamma and Beta Functions, Journal of Nonlinear Mathematical Physics, Volume 12, Number 1 (2005), 118-134. DOI: https://doi.org/10.2991/jnmp.2005.12.1.10
S. S. Dragomir, R. P. Agarwal, and N. S. Barnett, Inequality for Beta and Gamma functions via some classical and new integral inequalities, J. Inequal., 5(2)(2000), 103-165. DOI: https://doi.org/10.1155/S1025583400000084
A. Fitouhi, K. Brahim, Some inequalities for the q-Beta and the q-Gamma functions via some q-integral inequalities , Applied Mathematics and computation, 204(2008), 385-394. DOI: https://doi.org/10.1016/j.amc.2008.06.055
G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Application, Vol 35 Cambridge Univ. Press, Cambridge, UK, 1990.
H. Gauchman, Integral Inequalities in q-Calculus, Computers and Mathematics with Applications, 47(2004), 281-300. DOI: https://doi.org/10.1016/S0898-1221(04)90025-9
F. H. Jackson, A generalization of the function Γ(n) and x n , Proc. Roy. Soc. London, (74)(1904), 64-72.
F. H. Jackson, On a q-Definite Integrals, Quarterly Journal of Pure and Applied Mathematics, 41(1910), 193-203.
V. G. Kac and P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, New York, (2002). DOI: https://doi.org/10.1007/978-1-4613-0071-7
T. H. Koornwinder, q-Special Functions, a Tutorial, in Deformation theory and quantum groups with applications to mathematical physics, M. Gerstenhaber and J. Stasheff (eds), Contemp. Math. 134, Amer.Math. Soc., (1992).
T. H. Koornwinder, Special Functions and q-Commuting Variables, in Special Functions, q-Series and related Topics, M. E. H. Ismail, D. R. Masson and M. Rahman (eds), Fields Institute Communications 14,
American Mathematical Society, (1997), pp. 131–166; arXiv:q-alg/9608008.
J. Thomae, Beitrage zur Theorie der durch die Heinesche Reihe, J. reine angew. Math., (70)(1869), 258-281. DOI: https://doi.org/10.1515/9783112389409-021
- NA
Similar Articles
- Rabha W. Ibrahim, An application of Lauricella hypergeometric functions to the generalized heat equations , Malaya Journal of Matematik: Vol. 2 No. 01 (2014): Malaya Journal of Matematik (MJM)
- S.S. Redhwan, S.L. Shaikh, M.S. Abdo, S.Y. Al-Mayyahi, Sadik transform and some result in fractional calculus , Malaya Journal of Matematik: Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 MJM

This work is licensed under a Creative Commons Attribution 4.0 International License.