Rocky Mountain Journal of Mathematics

Some identities involving special numbers and moments of random variables

Taekyun Kim, Yonghong Yao, Dae San Kim, and Hyuck-In Kwon

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In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here, the related special numbers are Stirling numbers of the first and second kinds, degenerate Stirling numbers of the first and second kinds, derangement numbers, higher-order Bernoulli numbers and Bernoulli numbers of the second kind.

Article information

Rocky Mountain J. Math., Volume 49, Number 2 (2019), 521-538.

Received: 14 June 2018
Revised: 12 September 2018
First available in Project Euclid: 23 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A19: Combinatorial identities, bijective combinatorics 11B83: Special sequences and polynomials

random variable moment Stirling number degenerate Stirling number derangement number


Kim, Taekyun; Yao, Yonghong; Kim, Dae San; Kwon, Hyuck-In. Some identities involving special numbers and moments of random variables. Rocky Mountain J. Math. 49 (2019), no. 2, 521--538. doi:10.1216/RMJ-2019-49-2-521.

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