Results 41 to 50 of about 34,757 (249)
Matrices related to the Bell polynomials
Linear Algebra and its Applications, 2007 AbstractIn this paper, we study the matrices related to the partial exponential Bell polynomials and those related to the Bell polynomials with respect to Ω. As a result, the factorizations of these matrices are obtained, which give unified approaches to the factorizations of many lower triangular matrices.
Weiping Wang +2 more
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Diagonal recurrence relations for the Stirling numbers of the first kind [PDF]
, 2015 In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.Comment: 7 ...
Qi, Feng
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A Special Class of Bell Polynomials [PDF]
Mathematics of Computation, 1980 We examine the integersV(n,k)V(n,k)defined by means of\[k!∑n=0∞V(n,k)xn/n!=[x(ex+1)−2(ex−1)]k,k!\sum \limits _{n = 0}^\infty {V(n,k){x^n}/n! = {{[x({e^x} + 1) - 2({e^x} - 1)]}^k},}\]and, in particular, we show how these integers are related to the Bernoulli, Genocchi and van der Pol numbers, and the numbers generated by the reciprocal ofex−x−1{e^x} - x
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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General identities on Bell polynomials
Computers & Mathematics with Applications, 2009 AbstractThe exponential partial Bell polynomials are polynomials in an infinite number of variables x1,x2,…, and it is well-known that some special combinatorial sequences, e.g., Stirling numbers of both kinds, Lah numbers and idempotent numbers, can be obtained from the Bell polynomials.
Tianming Wang, Weiping Wang
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A new family of Apostol–Genocchi polynomials associated with their certain identities
Applied Mathematics in Science and Engineering, 2023 In this paper, we provide a generating function for mix type Apostol–Genocchi polynomials of order η associated with Bell polynomials. We also derive certain important identities of Apostol Genocchi polynomials of order η based on Bell polynomials, such ...
Nabiullah Khan +3 more
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On Generalized Class of Bell Polynomials Associated with Geometric Applications
AxiomsIn this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to
Rashad A. Al-Jawfi +2 more
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New Bell–Sheffer Polynomial Sets [PDF]
Axioms, 2018 In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them, have been studied. The method used in previous articles, and even in the present one, traces back to preceding results by Dattoli and Ben Cheikh on the monomiality principle, showing the possibility to derive ...
P. Natalini, P. E. Ricci
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On new identities for Bell's polynomials
Discrete Mathematics, 2005 AbstractIn this work, we propose two new methods for the determination of new identities for Bell's polynomials. The first method is based on the Lagrange inversion formula, and the second is based on the binomial sequences. These methods allow the easy recovery of known identities and deduction of some new identities of these polynomials.
Sadek Bouroubi, Moncef Abbas
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