On the k-gamma q-distribution

Rafael Díaz; Camilo Ortiz; Eddy Pariguan

Open Mathematics (2010)

  • Volume: 8, Issue: 3, page 448-458
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Rafael Díaz, Camilo Ortiz, and Eddy Pariguan. "On the k-gamma q-distribution." Open Mathematics 8.3 (2010): 448-458. <http://eudml.org/doc/268940>.

@article{RafaelDíaz2010,
abstract = {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.},
author = {Rafael Díaz, Camilo Ortiz, Eddy Pariguan},
journal = {Open Mathematics},
keywords = {q-Calculus; Gamma distribution; q-combinatorics; Mellin transform; Prochhammer -symbol},
language = {eng},
number = {3},
pages = {448-458},
title = {On the k-gamma q-distribution},
url = {http://eudml.org/doc/268940},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Rafael Díaz
AU - Camilo Ortiz
AU - Eddy Pariguan
TI - On the k-gamma q-distribution
JO - Open Mathematics
PY - 2010
VL - 8
IS - 3
SP - 448
EP - 458
AB - 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.
LA - eng
KW - q-Calculus; Gamma distribution; q-combinatorics; Mellin transform; Prochhammer -symbol
UR - http://eudml.org/doc/268940
ER -

References

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  2. [2] Callan D., A combinatorial survey of identities for the double factorial, preprint available at http://arxiv.org/abs/0906.1317 
  3. [3] Cheung P., Kac V, Quantum Calculus, Springer-Verlag, Berlin, 2002 
  4. [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 Zbl1225.33017
  5. [5] Díaz R., Pariguan E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 2007, 15, 179–192 Zbl1163.33300
  6. [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 Zbl1166.60007
  7. [7] Diaz R., Pariguan E., Super, Quantum and Non-Commutative Species, Afr. Diaspora J. Math, 2009, 8, 90–130 Zbl1239.16001
  8. [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 Zbl1075.33010
  9. [9] George G., Mizan R., Basic Hypergeometric series, Cambridge Univ. Press, Cambridge, 1990 Zbl0695.33001
  10. [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. [11] Kokologiannaki C.G., Properties and Inequalities of Generalized k-Gamma, Beta and Zeta Functions, Int. J. Contemp. Math. Sciences, 2010, 5, 653–660 Zbl1202.33003
  12. [12] Kuba M., On Path diagrams and Stirling permutations, preprint available at http://arxiv4.library.cornell.edu/abs/0906.1672 
  13. [13] Mansour M., Determining the k-Generalized Gamma Function Γk(x) by Functional Equations, Int. J. Contemp. Math. Sciences, 2009, 4, 1037–1042 Zbl1186.33002
  14. [14] Zeilberger D., Enumerative and Algebraic Combinatorics, In: Gowers T. (Ed.), The Princeton Companion to Mathematics, Princeton University Press, Princeton, 2008 Zbl1242.00016

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