Results 151 to 160 of about 30,485 (178)

The Arithmetic of Bell and Stirling Numbers

American Journal of Mathematics, 1948
Symbolic methods are used to obtain many of the properties of the Bell and Stirling numbers [cf. \textit{E. T. Bell}, Am. J. Math. 61, 89--101 (1939; Zbl 0020.10402)] modulo \(p\), a prime.
Becker, H. W., Riordan, John
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Degenerate r-Stirling Numbers and r-Bell Polynomials

Russian Journal of Mathematical Physics, 2018
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Kim, T., Yao, Y., Kim, D. S., Jang, G.-W.   +3 more
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Degenerate Stirling numbers and a family of Bell polynomials

MATHEMATICA, 2022
In this paper, we employ generating functions' techniques to obtain some identities involving degenerate Bell polynomials, multivariate Bell polynomials, and Carlitz degenerate Stirling numbers. Moreover, we obtain some formulas related to an explicit representation and recurrence relations for Lah polynomials.
Madjid Sebaoui, Ghania Guettai, Difalah Laissaoui, Mourad Rahmani   +3 more
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EVOLUTIONARY MATHEMATICS AND SCIENCE FOR GENERAL FAMOUS NUMBERS: STIRLING-EULER-LAH-BELL

2021
We first introduce Pascal, Stirling, Eulerian, Lah and Bell numbers via sorting, then generalize Stirling numbers of both kinds [■(n@k)], {■(n@k)}, Eulerian numbers of two orders 〈■(n@k)〉, 〈〈■(n@k)〉 〉, Lah numbers L(n,k)=∑_(j=1)^n▒[■(n@j)] {■(j@k)} and ∑_(k=0)^(n-1)▒〖2^k 〈■(n@k)〉 〗=∑_(k=1)^n▒(∑_(j-1)^(k+1)▒[■(k+1@j)] ){■(n@k)} , the right-hand side of ...
Chang, Leon, Tsao, Hung-ping, Tsao, Hung-ping   +2 more
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Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers

Journal of Mathematical Physics, 2015
We resolve the normal ordering problem for symmetric (Dˆ+Dˆ−)n and asymmetric (Dˆ+rDˆ−)n strings of the nonlinear deformed ladder operators Dˆ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N{(Dˆ+Dˆ−)n} and N{(Dˆ+rDˆ−)n}, where in N ...
A. N. F. Aleixo, A. B. Balantekin
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The ladder operator normal ordering problem for quantum confined systems and the generalization of the Stirling and Bell numbers

Journal of Physics A: Mathematical and Theoretical, 2009
We solve the normal ordering problem for the ladder operators and for strings in the form for supersymmetric and shape-invariant potential systems, with r, s and n positive integers. We provide exact and explicit expressions for their normal form , where in all are at the right side, and find that the solution involves an expansion coefficients ...
A N F Aleixo, A B Balantekin
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Ladder operators' normal ordering problem for quantum-deformed systems and the (q,p)-generalization of the Stirling and Bell numbers

Journal of Physics A: Mathematical and Theoretical, 2010
We resolve the ladder operators normal ordering problem for strings in the form for (q, p)-deformed supersymmetric and shape-invariant potential systems, where n is a positive integer. We provide exact and explicit expressions for their normal form , where in all are at the right-hand side, and find that the solution involves expansion-coefficients ...
A N F Aleixo, A B Balantekin
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BELL, BERNOULLI, CAUCHY, HARMONIC AND STIRLING NUMBERS

Algebras Groups and Geometries, 2023
S. Vidal-Beltran, M. Muniru Iddrisu, A. Hernandez-Galeana, J. Lopez-Bonilla   +3 more
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Generalizations of Stirling-like and Bell-like Numbers

2023
Eszter Gyimesi, Gábor Nyul, Gabriella Rácz   +2 more
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