Results 1 to 10 of about 116 (110)
An extension of the bell polynomials
Computers and Mathematics With Applications, 2004 The authors introduce an extension of Bell polynomials, also called ``partition polynomials''. For a given integer \(M\) they define a generalized Bell polynomial \(Y_n^{[M-1]}\) as representing the \(n\)th derivative of the composite function \(\Phi(t) := f_{(1)}(f_{(2)}(\cdots(f_{(M)}(t))))\), where the functions \(f_{(M)}\), \dots, \(f_{(2)}\), \(f_{
P Natalini
exaly +5 more sources
Bell-Based Bernoulli Polynomials with Applications [PDF]
Axioms, 2021 In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order α and investigate multifarious correlations and formulas ...
Uğur Duran +2 more
exaly +5 more sources
General identities on Bell polynomials
Computers and Mathematics With Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiping Wang
exaly +2 more sources
Journal of Approximation TheoryIn this paper, generalized Bell polynomials $(\Be_n^ϕ)_n$ associated to a sequence of real numbers $ϕ=(ϕ_i)_{i=1}^\infty$ are introduced. Bell polynomials correspond to $ϕ_i=0$, $i\ge 1$. We prove that when $ϕ_i\ge 0$, $i\ge 1$: (a) the zeros of the generalized Bell polynomial $\Be_n^ϕ$ are simple, real and non positive; (b) the zeros of $\Be_{n+1}^ϕ ...
Antonio J Duran
exaly +3 more sources
Bell polynomials and binomial type sequences
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Miloud Mihoubi
exaly +3 more sources
Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials [PDF]
Advances in Difference Equations, 2021 AbstractThe nth r-extended Lah–Bell number is defined as the number of ways a set with $n+r$ n + r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks.
Taekyun Kim +4 more
openaire +3 more sources
On Generalized Bell Polynomials [PDF]
Discrete Dynamics in Nature and Society, 2011 It is shown that the sequence of the generalized Bell polynomials Sn(x) is convex under some restrictions of the parameters involved. A kind of recurrence relation for Sn(x) is established, and some numbers related to the generalized Bell numbers and their properties are investigated.
Roberto B. Corcino, Cristina B. Corcino
openaire +3 more sources
Laguerre‐type Bell polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We develop an extension of the classical Bell polynomials introducing the Laguerre‐type version of this well‐known mathematical tool. The Laguerre‐type Bell polynomials are useful in order to compute the nth Laguerre‐type derivatives of a composite function. Incidentally, we generalize a result considered by L.
Pierpaolo Natalini, Paolo E. Ricci
openaire +4 more sources
The partial r-Bell polynomials [PDF]
Afrika Matematika, 2017 In this paper, we show that the r-Stirling numbers of both kinds, the r-Whitney numbers of both kinds, the r-Lah numbers and the r-Whitney-Lah numbers form particular cases of family of polynomials forming a generalization of the partial Bell polynomials. We deduce the generating functions of several restrictions of these numbers.
Mihoubi, Miloud, Rahmani, Mourad
openaire +2 more sources
New Properties on Degenerate Bell Polynomials [PDF]
Complexity, 2021 The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate versions of the Bell numbers and polynomials. We derive some new identities and properties of those numbers and polynomials that are associated with the degenerate Stirling numbers of both kinds.
Taekyun Kim 0001 +4 more
openaire +2 more sources