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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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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

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.
T. Apostol
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q‐Bernoulli numbers and polynomials

Mathematische Nachrichten, 1958
W. Al-salam
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Identities for Bernoulli polynomials and Bernoulli numbers

Archiv der Mathematik, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Kwong, Man Kam
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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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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

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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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 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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