Results 21 to 30 of about 65 (62)

Improved bounds on Bell numbers and on moments of sums of random variables [PDF]

, 2010
We provide bounds for moments of sums of sequences of independent random variables. Concentrating on uniformly bounded nonnegative random variables, we are able to improve upon previous results due to Johnson et al. [10] and Latała [12].
Berend, Daniel, Tassa, Tamir
core   +1 more source

Recurrence for probabilistic extension of Dowling polynomials

Open Mathematics
Spivey found a remarkable recurrence relation for Bell numbers, which was generalized to that for Bell polynomials by Gould-Quaintance. The aim of this article is to generalize their recurrence relation for Bell polynomials to that for the probabilistic ...
Ma Yuankui, Kim Taekyun, Kim Dae San, Xu Rongrong   +3 more
doaj   +1 more source

Probabilistic degenerate poly-Bell polynomials associated with random variables

Mathematical and Computer Modelling of Dynamical Systems
Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable [Formula: see ...
Pengxiang Xue, Yuankui Ma, Taekyun Kim, Dae San Kim, Wenpeng Zhang   +4 more
doaj   +1 more source

Some Identities of the probabilistic higher order frobenius-euler polynomials and their applications

Mathematical and Computer Modelling of Dynamical Systems
Recently, there has been significant research on the generalization of various numbers using probabilistic methods. In this paper, we introduce the probabilistic higher order Frobenius-Euler polynomials which are a generalization of Frobenius-Euler ...
Jin-Woo Park, Sangbeom Park, Sang Jo Yun, Jongkyum Kwon   +3 more
doaj   +1 more source

Some representations for inverse rising factorial moments

Mathematical and Computer Modelling of Dynamical Systems
Inverse rising factorial moments [Formula: see text] are fundamental quantities for positive integer-valued random variables, with broad applications in probability and combinatorics.
Xiaoxue Li, Yuankui Ma, Taekyun Kim, Dae San Kim   +3 more
doaj   +1 more source

Identities involving degenerate stirling numbers of the second kind

Mathematical and Computer Modelling of Dynamical Systems
Building on Carlitz’s foundational work with degenerate Euler and Bernoulli polynomials, recent research has introduced and studied various degenerate special numbers and polynomials.
Taekyun Kim, Dae San Kim, Murad Khalil, Kyo-Shin Hwang   +3 more
doaj   +1 more source

On a generalization of derangement polynomials and numbers

Demonstratio Mathematica
In T. Kim, D. S. Kim, and D. V. Dolgy, Probabilistic derangement numbers and polynomials, Math. Comput. Model. Dyn. Syst. 31 (2025), no. 1, 2529188, Kim-Kim defined the probabilistic derangement polynomials and numbers and found some properties of those ...
Yun Sang Jo, Park Jin-Woo
doaj   +1 more source

Probabilistic degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
Recently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin.
Lingling Luo, Taekyun Kim, Dae San Kim, Yuankui Ma   +3 more
doaj   +1 more source

Series involving degenerate harmonic numbers and degenerate Stirling numbers

Applied Mathematics in Science and Engineering
Recently, degenerate harmonic numbers and degenerate hyperharmonic numbers are introduced by Kim-Kim. In this paper, we study the series involving the degenerate harmonic numbers and degenerate Stirling numbers and investigate those properties.
Lingling Luo, Yuankui Ma, Taekyun Kim, Rongrong Xu   +3 more
doaj   +1 more source

Evaluation of cauchy polynomials via degenerate r-Stirling numbers

Mathematical and Computer Modelling of Dynamical Systems
In this paper, within the framework of unsigned degenerate [Formula: see text]-Stirling numbers, we establish connections among Cauchy polynomials, degenerate Bernoulli polynomials, and degenerate hyperharmonic numbers.
Zhuoyu Chen, Yuankui Ma, Taekyun Kim, Dae San Kim, Yanan Hei   +4 more
doaj   +1 more source