Some identities involving special numbers and moments of random variables
Taekyun Kim, Yonghong Yao, Dae San Kim, Hyuck-In Kwon
TL;DR
This paper derives identities involving special numbers such as Stirling, derangement, and Bernoulli numbers by utilizing generating functions of moments of specific random variables.
Contribution
The paper introduces new identities linking special numbers with moments of random variables using generating functions, expanding the theoretical understanding of these mathematical objects.
Findings
Derived identities involving Stirling, derangement, and Bernoulli numbers.
Connected special numbers with moments of random variables through generating functions.
Enhanced the theoretical framework relating combinatorial numbers and probability.
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.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Advanced Combinatorial Mathematics