Results 41 to 50 of about 383 (66)

Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers

Acta Universitatis Sapientiae: Mathematica, 2016
In the paper, the authors find several identities, including a new recurrence relation for the Stirling numbers of the first kind, involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers.
Qi Feng, Shi Xiao-Ting, Liu Fang-Fang
doaj   +1 more source

Investigating Exponential and Geometric Polynomials with Euler-Seidel Algorithm [PDF]

, 2010
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers.
Dil, Ayhan, Kurt, Veli
core  

Some identities on derangement and degenerate derangement polynomials

, 2017
In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number.
AM Garsia, DS Kim, J-L Lavoie, JB Remmel, L Carlitz, ML Wachs, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, W Heise   +14 more
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A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers

Demonstratio Mathematica
In this study, we introduce the λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers in the view of degenerate version, respectively.
Kim Taekyun, Kim Hye Kyung
doaj   +1 more source

Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations

, 2016
In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ...
Feng Qi (祁锋), Bai-Ni Guo (郭白妮)
semanticscholar   +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

The $r$-Bell numbers [PDF]

, 2010
The notion of generalized Bell numbers has appeared in several works but there is no systematic treatise on this topic. In this paper we fill this gap. We discuss the most important combinatorial, algebraic and analytic properties of these numbers which ...
Mezo, Istvan
core   +1 more source

On Multi-Order Logarithmic Polynomials and their Explicit Formulas, Recurrence Relations, and Inequalities

, 2017
In the paper, the author introduces the notions “multi-order logarithmic numbers” and “multi-order logarithmic polynomials”, establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faà di Bruno formula and two ...
Feng Qi (祁锋)
semanticscholar   +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
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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