Moments of infinite convolutions of symmetric Bernoulli distributions

Authors:
C. Escribano;M. A. Sastre;E. Torrano
Affiliations:
Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain;Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

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Abstract

We study the infinite convolution of symmetric Bernoulli distributions associated to a parameter r. We obtain an explicit formula for the moments as a function of Bernoulli numbers and conditioned partitions. Applying this formula we obtain the moments as a quotient of polynomials in the parameter r. The leading coefficient of the numerator is related to the asymptotic behavior of the moments and, unexpectedly, this coefficients are the absolute values of Euler numbers.