Results 11 to 20 of about 35,784 (255)
Some identities of Lah–Bell polynomials [PDF]
Advances in Difference Equations, 2020 Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n.
Yuankui Ma +4 more
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Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials [PDF]
Advances in Difference Equations, 2021 The 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
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Degenerate poly-Bell polynomials and numbers [PDF]
Advances in Difference Equations, 2021 Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials.
Taekyun Kim, Hye Kyung Kim
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$r-$Bell polynomials in combinatorial Hopf algebras
Comptes Rendus. Mathématique, 2016 We introduce partial $r$-Bell polynomials in three combinatorial Hopf algebras. We prove a factorization formula for the generating functions which is a consequence of the Zassenhauss formula.Comment: 7 ...
Chouria, Ali, Luque, Jean-Gabriel
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Some identities involving derangement polynomials and r-Bell polynomials
AIMS Mathematics, 2023 In this paper two kinds of identities involving derangement polynomials and $ r $-Bell polynomials were established. The identities of the first kind extended the identity on derangement numbers and Bell numbers due to Clarke and Sved and its ...
Aimin Xu
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Generalized Bell polynomials [PDF]
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. Durán
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Bell Polynomials and Nonlinear Inverse Relations [PDF]
The Electronic Journal of Combinatorics, 2021 By means of the Lagrange expansion formula, we establish a general pair of nonlinear inverse series relations, which are expressed via partial Bell polynomials with the connection coefficients involve an arbitrary formal power series. As applications, two examples are presented with one of them recovering the difficult theorems discovered recently by ...
Wenchang Chu
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Polynomial Bell Inequalities [PDF]
Physical Review Letters, 2016 9 pages (including appendix)
Rafael Chaves
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Probabilistic degenerate central Bell polynomials
Mathematical and Computer Modelling of Dynamical SystemsAssume that [Formula: see text] is a random variable whose moment generating function exists in a neighbourhood of the origin. In this paper, we study the probabilistic degenerate central Bell polynomials associated with [Formula: see text], as ...
Li Chen +4 more
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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
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