Results 11 to 20 of about 10,388 (168)
Arithmetical properties of double Möbius-Bernoulli numbers
Open Mathematics, 2019 Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x).
Bayad Abdelmejid, Kim Daeyeoul, Li Yan
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Some Identities of the Degenerate Multi-Poly-Bernoulli Polynomials of Complex Variable
Journal of Function Spaces, 2021 In this paper, we introduce degenerate multi-poly-Bernoulli polynomials and derive some identities of these polynomials. We give some relationship between degenerate multi-poly-Bernoulli polynomials degenerate Whitney numbers and Stirling numbers of the ...
G. Muhiuddin +3 more
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Advances in Difference Equations, 2019 In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 ...
Dae San Kim +3 more
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An Expression for Bernoulli Numbers [PDF]
Proceedings of the Glasgow Mathematical Association, 1953 In Muir's Theory of Determinants, Vol. III, pp. 232–237, there will be found accounts of papers by H. Nägelsbach, J. Hammond and J. W. L. Glaisher, in which expressions for the Bernoulli numbers are obtained in terms of determinants. In the present paper an expression for Bn will be derived which appears to be new, but which is very like some of those ...
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Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0
Abstract and Applied Analysis, 2011 Recently, Kim (2011) has introduced the q-Bernoulli numbers with weight α. In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated ...
T. Kim, J. Choi, Y. H. Kim
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Fast Calculation of Bernoulli Numbers
Современные информационные технологии и IT-образование, 2019 Bernoulli numbers are often found in mathematical analysis, number theory, combinatorics, and other areas of mathematics. In some monographs on number theory there are separate chapters devoted only to Bernoulli numbers and their properties.
Rustem R. Aidagulov, Sergei T. Glavatsky
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A Parametric Type of Cauchy Polynomials with Higher Level
Axioms, 2021 There are many kinds of generalizations of Cauchy numbers and polynomials. Recently, a parametric type of the Bernoulli numbers with level 3 was introduced and studied as a kind of generalization of Bernoulli polynomials.
Takao Komatsu
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Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
Mathematics, 2016 In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli ...
Feng Qi, Bai-Ni Guo
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Congruences for Bernoulli numbers and Bernoulli polynomials
Discrete Mathematics, 1997 The Bernoulli numbers and polynomials are defined by \(B_0=1\), \(\sum^{n-1}_{k=0}{n\choose k} B_k= 0\) \((n=2,3,\dots)\) and \(B_n(x)= \sum^n_{k=0}{n\choose k} B_{n-k} x^k\), respectively. Two basic congruences for Bernoulli numbers are the Kummer congruences (used in the theory of Fermat's last theorem) and the von Staudt-Clausen theorem. There exist
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Probabilistic poly-Bernoulli numbers
Mathematical and Computer Modelling of Dynamical SystemsAssume that is Y a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study probabilistic poly-Bernoulli numbers associated with Y, as probabilistic extensions of poly-Bernoulli numbers ...
Wencong Liu +3 more
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