Results 81 to 90 of about 51,714 (196)

On degenerate multi-poly-derangement polynomials and numbers

Applied Mathematics in Science and Engineering
The problem of counting derangements was begun in 1708 by Pierre R[Formula: see text]mond de Montmort (see [Carlitz. The number of derangements of a sequence with given specification. Fibonacci Quart. 1978;16:255–258], [Clarke and Sved.
Sang Jo Yun, Jin-Woo Park
doaj   +1 more source

Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

Advances in Difference Equations, 2019
We show that the Stirling numbers of the first and second kind can be represented in terms of moments of appropriate random variables. This allows us to obtain, in a unified way, a variety of old and new explicit expressions and integral representations ...
José A. Adell, Alberto Lekuona
doaj   +1 more source

Combinatorial interpretations of the Jacobi-Stirling numbers

, 2009
The Jacobi-Stirling numbers of the first and second kinds were introduced in 2006 in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers.
Gelineau, Yoann, Zeng, Jiang
core   +1 more source

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   +1 more source

Combinatorial identities associated with new families of the numbers and polynomials and their approximation values

, 2017
Recently, the numbers $Y_{n}(\lambda )$ and the polynomials $Y_{n}(x,\lambda)$ have been introduced by the second author [22]. The purpose of this paper is to construct higher-order of these numbers and polynomials with their generating functions.
Kucukoglu, Irem, Simsek, Yilmaz
core  

Three closed forms for convolved Fibonacci numbers

Results in Nonlinear Analysis, 2020
In the paper, by virtue of the Faà di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three
Feng Qi
doaj  

Variations of Central Limit Theorems and Stirling numbers of the First Kind

, 2022
Bernhard Heim, Markus Neuhäuser
openalex   +2 more sources

Some Sums Involving Generalized Harmonic and r-Derangement Numbers

Cumhuriyet Science Journal
In this paper, we derive some sums involving generalized harmonic and r-derangement numbers by using generating functions of these numbers and some combinatorial identities. The relationship between Daehee numbers and generalized harmonic numbers of rank
Sibel Koparal
doaj   +1 more source

On the degenerate negative λ-binomial and Poisson random variables from degenerate special polynomials

Mathematical and Computer Modelling of Dynamical Systems
In this paper, we investigate the theory and applications of negative λ-binomial random variable with parameter [Formula: see text] and Poisson random variable with parameter [Formula: see text].
Jongkyum Kwon, Sangbeom Park, Jin-Woo Park   +2 more
doaj   +1 more source

Asymptotic approximation with Stancu Beta operators

Journal of Numerical Analysis and Approximation Theory, 1998
The concern of this paper is a beta type operator \(L_n\) recently introduced by D.D. Stancu. We present the complete asymptotic expansion for \(L_n\) as \(n\) tends to infinity. All coefficients of \(n^{-k} \ (k=1,2, \ldots)\) are calculated explicitly
Ulrich Abel
doaj   +2 more sources