Moments of infinite convolutions of symmetric Bernoulli distributions
type: Item
instance of: scholarly article
title: Moments of infinite convolutions of symmetric Bernoulli distributions
zbMATH Open document ID: 1020.44010
DOI: 10.1016/S0377-0427(02)00595-2
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-22T00:00:00Z
review text: For any number \(r\in (1/2,1)\) the authors consider the sets \(\{r^n,-r^n\}\), \(n= 0,1,\dots\), and the corresponding Bernoulli distributions \(\mu_{r,n}\). Then they define the infinitely convolved symmetric Bernoulli measure \[ \mu_r= \lim_{n\to\infty} (\mu_{r,0}* \mu_{r,1}*\cdots* \mu_{r,n}). \] The main result of the paper is an explicit formula for the moments \(S_k\) of this measure in terms of Bernoulli numbers. The moments can also be written as quotients of certain polynomials in the parameter \(r\). It is shown that the leading coefficient of the numerator in \(S_k\) are the absolute values of the Euler numbers \(E_k\).
Mathematics Subject Classification ID: 44A60
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1915233
zbMATH Keywords: infinite Bernoulli convolution
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: exponential generating function
zbMATH Keywords: Euler numbers
zbMATH Keywords: Bernoulli distributions
zbMATH Keywords: Bernoulli measure
zbMATH Keywords: moments
zbMATH Keywords: Bernoulli numbers
author: C. Escribano
author: M. Asunción Sastre
author: E. Torrano
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915233