On the k-gamma q-distribution

• Autorzy: Rafael Díaz , Camilo Ortiz , Eddy Pariguan
• Języki publikacji: EN

Abstrakty

EN

We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Díaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma distribution.

Słowa kluczowe

EN

q-Calculus; Gamma distribution; q-combinatorics

Kategorie tematyczne

• 05C30: Enumeration in graph theory
• 05A30: q -calculus and related topics
• 60E05: Distributions: general theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 3
• Strony: 448-458

Daty

wydano

2010-06-01

online

2010-05-30

Twórcy

autor

Rafael Díaz

• Universidad Sergio Arboleda,

autor

Camilo Ortiz

• Pontificia Universidad Javeriana,

autor

Eddy Pariguan

• Pontificia Universidad Javeriana,

Bibliografia

• [1] Andrews G., Askey R., Roy R., Special functions, Cambridge University Press, Cambridge, 1999
• [2] Callan D., A combinatorial survey of identities for the double factorial, preprint available at http://arxiv.org/abs/0906.1317
• [3] Cheung P., Kac V, Quantum Calculus, Springer-Verlag, Berlin, 2002
• [4] De Sole A., Kac V., On integral representations of q-gamma and q-beta functions, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei 9. Mat. Appl., 2005, 16, 11–29
• [5] Díaz R., Pariguan E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 2007, 15, 179–192
• [6] Díaz R., Pariguan E., On the Gaussian q-distribution, J. Math. Anal. Appl., 2009, 358, 1–9 http://dx.doi.org/10.1016/j.jmaa.2009.04.046
• [7] Diaz R., Pariguan E., Super, Quantum and Non-Commutative Species, Afr. Diaspora J. Math, 2009, 8, 90–130
• [8] Díaz R., Teruel C, q, k-generalized gamma and beta functions, J. Nonlinear Math. Phys., 2005, 12, 118–134 http://dx.doi.org/10.2991/jnmp.2005.12.1.10
• [9] George G., Mizan R., Basic Hypergeometric series, Cambridge Univ. Press, Cambridge, 1990
• [10] Gessel I., Stanley R, Stirling polynomials, J. Combin. Theory Ser. A, 1978, 24, 24–33 http://dx.doi.org/10.1016/0097-3165(78)90042-0
• [11] Kokologiannaki C.G., Properties and Inequalities of Generalized k-Gamma, Beta and Zeta Functions, Int. J. Contemp. Math. Sciences, 2010, 5, 653–660
• [12] Kuba M., On Path diagrams and Stirling permutations, preprint available at http://arxiv4.library.cornell.edu/abs/0906.1672
• [13] Mansour M., Determining the k-Generalized Gamma Function Γk(x) by Functional Equations, Int. J. Contemp. Math. Sciences, 2009, 4, 1037–1042
• [14] Zeilberger D., Enumerative and Algebraic Combinatorics, In: Gowers T. (Ed.), The Princeton Companion to Mathematics, Princeton University Press, Princeton, 2008

Identyfikatory

DOI

10.2478/s11533-010-0029-0