Proof of a conjecture by Gazeau et al. using the Gould-Hopper polynomials

We provide here some probabilistic interpretations of the generalized binomial distributions proposed by Gazeau et al. ["Generating functions for generalized binomial distributions," J. Math. Phys. 53, 103304 (2012)]. In the second part, we prove the "strong conjecture" expressed by Gazeau et al. about the coefficients of the Taylor expansion of the exponential of a polynomial. The proof relies mainly on properties of the Gould-Hopper polynomials. (C) 2013 AIP Publishing LLC.


Published in:
Journal Of Mathematical Physics, 54, 7
Year:
2013
Publisher:
Melville, Amer Inst Physics
ISSN:
0022-2488
Laboratories:




 Record created 2013-10-01, last modified 2018-09-13


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