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Symmetric generalized binomial distributions
1. E. M. F. Curado, J. P. Gazeau, and L. M. C. S. Rodrigues, “On a generalization of the binomial distribution and its Poisson-like limit,” J. Stat. Phys. 146, 264–280 (2012).
2. H. Bergeron, E. M. F. Curado, J. P. Gazeau, and L. M. C. S. Rodrigues, “Generating functions for generalized binomial distributions,” J. Math. Phys. 53, 103304 (2012).
3. E. M. F. Curado, J. P. Gazeau, and L. M. C. S. Rodrigues, “Non-linear coherent states for optimizing quantum information, Proceedings of the Workshop on Quantum Nonstationary Systems, October 2009, Brasilia. Comment section (CAMOP),” Phys. Scr. 82, 038108 (2010).
5. J.-P. Gazeau, Coherent States in Quantum Physics (Wiley, 2009).
8. B. de Finetti, Atti Accad. Naz. Lincei, Mem., Cl. Sci. Fis., Mat. Nat. 4, 251299 (1931);
8.D. Heath and W. Sudderth, Am. Stat. 30, 188 (1976).
10.In our articles, the terms generalized binomial or binomial-like or deformed binomial distribution refer to mathematical expressions like (2) in which xn are non-negative real arbitrary numbers. In most papers devoted to probability and statistics in which such terms are used, their meaning is a lot more restrictive and concerns counting combinatorics and integer numbers.
12. S. Roman, The Umbral Calculus (Dover Publications, 2005);
12.R. Mullin and G. C. Rota A, “Theory of binomial enumeration,” in Graph Theory and its Applications (Academic Press, New York, 1970);
12.A. Di Bucchianico, Probabilistic and Analytical Aspects of the Umbral Calculus, CWI Tracts Vol. 119 (Centrum voor Wiskunde en Informatica, Amsterdam, 1997), pp. 1–148.
13. L. Comtet, Advanced Combinatorics (Reidel, 1974).
14.We are grateful to the referee for mentioning this point.
15. N. Johnson, S. Kotz, and A. W. Kempf, Univariate Discrete Distributions, 2nd ed. (John Wiley and Sons, 1992), p. 239.
17. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, USA, 1994).
18. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, 10th ed., Applied Mathematical Series Vol. 55 (National Bureau of Standards, Washington, 1972).
19. H. Bergeron
, E. M. F. Curado
, J. P. Gazeau
, and L. M. C. S. Rodrigues
, “A note about combinatorial sequences and incomplete gamma function
,” e-print arXiv:1309.6910v1
20. J. Aczél and J. Dhombres, Functional equations in several variables, Cambridge University Press, New York, 1989.
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