Results 91 to 100 of about 1,852 (188)

BELL PERMUTATIONS AND STIRLING NUMBERS INTERPOLATION

, 1999
A family of number sequences which interpolates the sequences of Bell numbers and n!
PERGOLA, ELISA, PINZANI, RENZO, G. LABELLE, P. LEROUX   +3 more
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Probabilistic degenerate r-Stirling numbers of the second and probabilistic degenerate r-Bell polynomials [PDF]

Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. We study the probabilistic degenerate r-Stirling numbers of the second kind associated with Y and the probabilistic degenerate r-Bell polynomials ...
Kim, Dae San, Kim, Taekyunj
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Asymptotics of stirling numbers of the second kind [PDF]

, 1972
A complete asymptotic development of the Stirling numbers S(N,K) of the second kind is obtained by the saddle point method previously employed by Moser and Wyman [Trans. Roy. Soc.
Wang, Peter C. C., Bleick, Willard Evan
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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

Recurrences of Stirling and Lah numbers via second kind Bell polynomial

Discrete Mathematics Letters, 2020
Summary: In the paper, by virtue of several explicit formulas for special values and a recurrence of the Bell polynomials of the second kind, the authors derive several recurrences for the Stirling numbers of the first and second kinds, for 1-associate Stirling numbers of the second kind, for the Lah numbers, and for the binomial coefficients.
Qi F., Natalini P., Ricci P. E.
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The ordered Bell numbers as weighted sums of odd or even Stirling numbers of the second kind

, 2021
For the Stirling numbers of the second kind $S(n,k)$ and the ordered Bell numbers $B(n)$, we prove the identity $\sum_{k=1}^{n/2} S(n,2k)(2k-1)! = B(n-1)$. An analogous identity holds for the sum over odd $k$'s.
openaire   +2 more sources

Stirling numbers and the operator

, 2020
El presente trabajo abarca los números de Stirling y su aparición en los polinomios exponenciales, también conocidos como polinomios de Bell. Dichos números fueron introducidos por el Matemático escocés James Stirling en el siglo XVIII, y presentan un ...
Cabas Avendaño, Sebastián Nicolay
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A new family of q-Bernstein polynomials: probabilistic viewpoint

Arab Journal of Basic and Applied Sciences
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming [Formula: see text] is a random variable satisfying moment conditions, we use the generating function of ...
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci   +2 more
doaj   +1 more source

Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions ^†

Mathematics
This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and ...
Feng Qi
doaj   +1 more source

Generalized Stirling numbers, exponential Riordan arrays and orthogonal polynomials [PDF]

, 2011
We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of
Hennessy, Aoife, Barry, Paul
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