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Runtime Monitoring of Static Fairness Properties

Henzinger TA, Karimi M, Kueffner K, Mallik K.   +3 more
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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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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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On the zeros of shifted Bernoulli polynomials

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ákos Pintér, Csaba Rakaczki
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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 Note on Bernoulli-Goss Polynomials

Canadian Mathematical Bulletin, 1984
AbstractIn an important series of papers ([3], [4], [5]), (see also Rosen and Galovich [1], [2]), D. Goss has developed the arithmetic of cyclotomic function fields. In particular, he has introduced Bernoulli polynomials and proved a non-existence theorem for an analogue to Fermat’s equation for regular “exponent”. For each odd prime p and integer n, l
Ireland, K., Small, D.
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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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Convolutions of Bernoulli and Euler Polynomials

Sarajevo Journal of Mathematics
By means of the generating function technique, several convolution identities are derived for the polynomials of Bernoulli and Euler.   2000 Mathematics Subject Classification.
CHU, Wenchang, ZHOU R. R.
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A New Formula for the Bernoulli Polynomials

Results in Mathematics, 2010
The author defines \(r\)-Whitney numbers \(w_{m,r}(n,k)\) and \(W_{m,r}(n,k)\) of the first and second kind by the equalities \[ m^nx^{\underline{n}}=\sum_{k=0}^nw_{m,r}(n,k)(mx+r)^k \] and \[ (mx+r)^n=\sum_{k=0}^nm^kW_{m,r}(n,k)x^{\underline{k}} \] with \(x^{\underline{n}}=x(x-1)\cdots(x-n+1)\) denoting falling factorials. These numbers are also given
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Generalization of Bernoulli polynomials

International Journal of Mathematical Education in Science and Technology, 2002
The Bernoulli polynomials are generalized and some properties of the resulting generalizations are presented.
Qi, Feng, Guo, Bai-Ni
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