## Rocky Mountain Journal of Mathematics

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

### Some identities involving special numbers and moments of random variables

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

#### Abstract

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

**Source**

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

**Dates**

Received: 14 June 2018

Revised: 12 September 2018

First available in Project Euclid: 23 June 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1561318391

**Digital Object Identifier**

doi:10.1216/RMJ-2019-49-2-521

**Mathematical Reviews number (MathSciNet)**

MR3973238

**Zentralblatt MATH identifier**

07079982

**Subjects**

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

**Keywords**

random variable moment Stirling number degenerate Stirling number derangement number

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1561318391