Results 211 to 220 of about 27,298 (248)

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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Probabilistic Bernoulli and Euler Polynomials

Russian Journal of Mathematical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, T., Kim, D. S.
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p-Bernoulli and geometric polynomials

International Journal of Number Theory, 2018
We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of [Formula: see text]-Bernoulli polynomials ...
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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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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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Bernoulli and Euler Polynomials

2021
Focus of this chapter are Bernoulli numbers and polynomials, and Euler numbers and polynomials in the complex domain. For the evaluation several methods can be used in dependence of the polynomial degree and argument: Direct integration, direct integration in combination with argument transformations, or expansions with respect to trigonometric series.
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Supercongruences involving Bernoulli polynomials

International Journal of Number Theory, 2016
Let [Formula: see text] be a prime, and let [Formula: see text] be a rational [Formula: see text]-adic integer. Let [Formula: see text] and [Formula: see text] denote the Bernoulli numbers and Bernoulli polynomials given by [Formula: see text] and [Formula: see text].
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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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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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