On the Gaussian q-distribution

Journal of Mathematical Analysis and Applications

Volumn 358, Issue 1, 2009, Pages 1-9

  Díaz, Rafael ^a   Pariguan, Eddy ^b  

^a UNIVERSIDAD DEL ROSARIO   (Colombia)

^b PONTIFICIA UNIVERSIDAD JAVERIANA   (Colombia)

Author keywords

Gaussian measure; q Calculus; q Combinatorics

Indexed keywords

EID: 67949111062     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.04.046     Document Type: Article

References (25)

1. Andrews G. The Theory of Partitions (1938), Cambridge Univ. Press, Cambridge
2. Andrews G., Askey R., and Roy R. Special Functions (1999), Cambridge Univ. Press, Cambridge
3. Blandín H., and Díaz R. Rational combinatorics. Adv. in Appl. Math. 40 (2008) 107-126
4. Bożejko M., Kümmerer B., and Speicher R. q-Gaussian processes: Non-commutative and classical aspects. Comm. Math. Phys. 185 (1997) 129-154
5. Bryc W. Classical versions of q-Gaussian processes: Conditional moments and Bell's inequality. Comm. Math. Phys. 219 (2001) 259-270
6. Bryc W., Matysiak W., and Szablowski P. Probabilistic aspects of al-Salam-Chihara polynomials. Proc. Amer. Math. Soc. 133 (2005) 1127-1134
7. Cheung P., and Kac V. Quantum Calculus (2002), Springer-Verlag, Berlin
8. De Sole A., and 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. 16 (2005) 11-29
9. Díaz R., and Pariguan E. An example of Feynman-Jackson integral. J. Phys. A 40 (2007) 1265-1272
10. Díaz R., and Pariguan E. Feynman-Jackson integrals. J. Nonlinear Math. Phys. 13 (2006) 365-376
11. Díaz R., and Pariguan E. On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. 15 (2007) 179-192
12. R. Díaz, E. Pariguan, Super, quantum and non-commutative species, arXiv:math.CT/0509674, preprint
13. Díaz R., and Teruel C. q, k-Generalized gamma and beta functions. J. Nonlinear Math. Phys. 12 (2005) 118-134
14. Gasper G., and Rahman M. Basic Hypergeometric Series (1990), Cambridge Univ. Press, Cambridge
15. In: Gell-Mann M., and Tsallis C. (Eds). Nonextensive Entropy: Interdisciplinary Applications (2004), Oxford Univ. Press, New York
16. van Leeuven H., and Maassen H. A q-deformation of the Gauss distribution. J. Math. Phys. 36 (1995) 4743-4756
17. Kupershmidt B. q-Probability: I. Basic discrete distributions. J. Nonlinear Math. Phys. 7 (2000) 73-93
18. Plastino A.R., and Plastino A. Non-extensive statistical mechanics and generalized Fokker-Planck equation. Phys. A 222 (1995) 347
19. Prato D., and Tsallis C. Nonextensive foundation of Lévy distributions. Phys. Rev. E 60 (1999) 2398
20. Tsallis C., and Bukman D. Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis. Phys. Rev. E 54 (1996) R2197
21. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52 (1988) 479-487
22. Tsallis C., Levy S.V.F., de Souza A.M.C., and Maynard R. Statistical-mechanical foundation of the ubiquity of Lévy distributions in nature. Phys. Rev. Lett. 75 (1995) 3589
23. Tsallis C., Levy S.V.F., de Souza A.M.C., and Maynard R. Statistical-mechanical foundation of the ubiquity of Lévy distributions in nature. Phys. Rev. Lett. 77 (1996) 5442 Erratum
24. S. Umarov, C. Tsallis, S. Steinberg, A generalization of the central limit theorem consistent with nonextensive statistical mechanics, arXiv:cond-mat/0603593, preprint
25. Zeilberger D. Proof of the refined alternating sing matrix conjecture. New York J. Math. 2 (1996) 59-68