Results 171 to 180 of about 18,359 (203)

The Integrality of the Values of Bernoulli Polynomials and of Generalised Bernoulli Numbers

Bulletin of the London Mathematical Society, 1997
\textit{G. Almkvist} and \textit{A. Meurman} [C. R. Math. Acad. Sci., Soc. R. Can. 13, 104-108 (1991; Zbl 0731.11014)] proved a result on the values of the Bernoulli polynomials at rational values of the argument. Subsequently \textit{B. Sury} [Bull. Lond. Math. Soc. 25, 327-329 (1993; Zbl 0807.11014)] and \textit{K. Bartz} and \textit{J. Rutkowski} [C.
Clarke, Francis, Slavutskii, I. Sh.
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Bernoulli Polynomials and Bernoulli Numbers

2002
In this chapter, we introduce a sequence of polynomials that is closely related to the h-antiderivative of polynomials and has many important applications.
Victor Kac, Pokman Cheung
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Generalized Bernoulli Polynomials and Numbers, Revisited

Mediterranean Journal of Mathematics, 2014
We describe with some new details the connection between generalized Bernoulli polynomials, Bernoulli polynomials and generalized Bernoulli numbers (Norlund polynomials). A new recursive and explicit formulae for these polynomials are derived.
Neven Elezović
exaly   +2 more sources

Formulas for Bernoulli Numbers and Polynomials

Results in Mathematics
Special polynomials and numbers possess much importance in multifarious areas of sciences such as physics, mathematics, applied sciences, engineering, and other related research fields covering differential equations, number theory, functional analysis, quantum mechanics, mathematical analysis, mathematical physics, and so on.
Ulrich Abel, Horst Alzer
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A class of polynomials and connections with Bernoulli’s numbers

The Journal of Analysis, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gradimir V. Milovanović, Yilmaz Simsek, Vladica S. Stojanović   +2 more
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Bernoulli Polynomials and Bernoulli Numbers

1973
The summing of the first n natural numbers, or Squares, or cubes, is a rather elementary problem in number theory and leads to the well known formulae $$\eqalign{ & \sum\limits_{n = 1}^N n \, = \,{{N(N + 1)} \over 2}, \cr & \sum\limits_{n = 1}^N {{n^2}} \, = \,{{N(N + 1)(2N + 1)} \over 6}, \cr & \sum\limits_{n = 1}^N {{n^3}} \, = \,{{{N^2}{{(N + 1)}
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The Value of Bernoulli Polynomials at Rational Numbers

Bulletin of the London Mathematical Society, 1993
For \(n\geq 1\), let \(B_ n(t)\) denote the \(n\)-th Bernoulli polynomial. \textit{G. Almkvist} and \textit{A. Meurman} [C. R. Math. Acad. Sci., Soc. R. Can. 13, No. 2/3, 104-108 (1991; Zbl 0731.11014)] proved that \(B_ n(h/k)- B_ n(0)\in (1/k^ n)\mathbb{Z}\) whenever \(h\) and \(k\) are positive integers. The author proves this in a shorter way.
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Bernoulli Numbers and Polynomials

1976
The oldest distribution is that defined by the Bernoulli polynomials, although of course their classical recurrence property was not called by that name.
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Identities for the Bernoulli and Euler numbers and polynomials.

Ars Comb., 2012
Summary: In this paper, we investigate some interesting identities on the Euler numbers and polynomials arising from their generating functions and difference operators. Finally, we give some properties of Bernoulli and Euler polynomials by using \(p\)-adic integral on \(\mathbb Z_p\).
Taekyun Kim 0001, B. Lee, S. H. Lee, Seog-Hoon Rim   +3 more
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A Primer on Bernoulli Numbers and Polynomials

Mathematics Magazine, 2008
(2008). A Primer on Bernoulli Numbers and Polynomials. Mathematics Magazine: Vol. 81, No. 3, pp. 178-190.
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