Results 11 to 20 of about 59 (58)
Sums of Powers and Special Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their ...
Boyadzhiev Khristo N.
doaj +1 more source
Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
doaj +1 more source
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 +2 more sources
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
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
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
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
doaj +1 more source
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
doaj +1 more source
Some representations for inverse rising factorial moments
Mathematical and Computer Modelling of Dynamical SystemsInverse rising factorial moments [Formula: see text] are fundamental quantities for positive integer-valued random variables, with broad applications in probability and combinatorics.
Xiaoxue Li +3 more
doaj +1 more source