Results 21 to 30 of about 371 (66)
Fourier series of functions involving higher-order ordered Bell polynomials
Open Mathematics, 2017 In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the ...
Kim Taekyun +3 more
doaj +1 more source
The k‐Augmented Pascal Matrix and Its Properties
Journal of Mathematics, Volume 2025, Issue 1, 2025.We define the k‐augmented Pascal matrix and present both a generalization and an alternative version of this matrix. We derive some properties of the defined matrices and establish a connection with generalized Stirling numbers and second‐order Eulerian numbers. Additionally, we provide a factorization of the k‐augmented Pascal matrix, highlighting its
Gonca Kizilaslan +2 more
wiley +1 more source
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 +14 more
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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
Recurrence for probabilistic extension of Dowling polynomials
Open MathematicsSpivey 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 +3 more
doaj +1 more source
, 2012 In the paper, the author establishes some identities which show that the functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients involving the ...
Andrews +5 more
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A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
Demonstratio MathematicaIn 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
, 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
Probabilistic degenerate poly-Bell polynomials associated with random variables
Mathematical and Computer Modelling of Dynamical SystemsLet [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 +4 more
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Some Identities of the probabilistic higher order frobenius-euler polynomials and their applications
Mathematical and Computer Modelling of Dynamical SystemsRecently, 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 +3 more
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