On moments of Cantor and related distributions
Pawe{\l} J. Szab{\l}owski
TL;DR
This paper derives recursive formulas for moments of infinite Bernoulli convolutions, relates different convolutions, and connects moments to classical sequences like Euler, Pell, and Lucas numbers, revealing new identities.
Contribution
It introduces simple recursive formulas for moments of infinite Bernoulli convolutions and links these moments to well-known number sequences, providing new identities and interpretations.
Findings
Recursive formulas for moments of Bernoulli convolutions
Connections between moments and Euler, Pell, Lucas numbers
New identities involving classical number sequences
Abstract
We provide several simple recursive formulae for the moment sequence of infinite Bernoulli convolution. We relate moments of one infinite Bernoulli convolution with others having different but related parameters. We give examples relating Euler numbers to the moments of infinite Bernoulli convolutions. One of the examples provides moment interpretation of Pell numbers as well as new identities satisfied by Pell and Lucas numbers.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Mathematical Theories and Applications · Advanced Mathematical Identities