Results 1 to 10 of about 52,395 (273)

Study on r-truncated degenerate Stirling numbers of the second kind [PDF]

Open Mathematics, 2022
The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some ...
Kim Taekyun, Kim Dae San, Kim Hyekyung
doaj   +6 more sources

Some identities related to degenerate Stirling numbers of the second kind [PDF]

Demonstratio Mathematica, 2022
The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
doaj   +3 more sources

Probabilistic multi-Stirling numbers of the second kind associated with random variables

Applied Mathematics in Science and Engineering
This paper investigates a probabilistic extension of the multi-Stirling numbers of the second kind and a ‘poly' version of the probabilistic degenerate Lah-Bell polynomials.
Xiangjing Liu, Yuankui Ma, Taekyun Kim, Dae San Kim, Yanan Hei   +4 more
doaj   +3 more sources

SOME REMARKS ABOUT STIRLING NUMBERS OF THE SECOND KIND

Human Research in Rehabilitation, 2013
In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas.
Ramiz Vugdalić, Fatih Destović
doaj   +5 more sources

Probabilistic Stirling Numbers of the Second Kind and Applications [PDF]

Journal of Theoretical Probability, 2020
Associated with each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided.
J. Adell
semanticscholar   +7 more sources

Multi-Stirling numbers of the second kind

Filomat, 2023
The multi-Stirling numbers of the second kind, the unsigned multi-Stirling numbers of the first kind, the multi-Lah numbers and the multi-Bernoulli numbers are all defined with the help of the multiple logarithm, and generalize respectively the Stirling ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
semanticscholar   +3 more sources

The Hadamard product of series with Stirling numbers of the second kind and other special numbers [PDF]

Electronic Journal of Mathematics, 2022
We evaluate in closed form a number of power series where the coefficients are products of Stirling numbers of the second kind and other special numbers or polynomials. The results include harmonic, hyperharmonic, derangement, Cauchy, Catalan numbers, zeta
Khristo N. Boyadzhiev, Robert Frontczak
doaj   +2 more sources

Close Encounters with the Stirling Numbers of the Second Kind [PDF]

Mathematics Magazine, 2012
Summary This is a short introduction to the theory of Stirling numbers of the second kind S(m, k) from the point of view of analysis. It is written as an historical survey centered on the representation of these numbers by a certain binomial transform ...
K. Boyadzhiev
semanticscholar   +4 more sources

Computing a family of probabilistic numbers in terms of probabilistic Stirling numbers of the second kind

Applied Mathematics in Science and Engineering
In this paper, we introduce the probabilistic Bernoulli numbers, Cauchy numbers, and Euler numbers of order α associated with the random variable Y, utilizing the generating function approach.
Aimin Xu
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Some results on p-adic valuations of Stirling numbers of the second kind

AIMS Mathematics, 2020
Let $n$ and $k$ be nonnegative integers. The Stirling number of the second kind, denoted by $S(n, k)$, is defined as the number of ways to partition a set of $n$ elements into exactly $k$ nonempty subsets and we have $$ S(n, k)=\frac{1}{k!}\sum_{i=0}^{k}(
Yulu Feng, Min Qiu
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