Results 201 to 210 of about 1,776 (233)

Novel Identities of Bernoulli Polynomials Involving Closed Forms for Some Definite Integrals

Symmetry, 2022
This paper presents new results of Bernoulli polynomials. New derivative expressions of some celebrated orthogonal polynomials and other polynomials are given in terms of Bernoulli polynomials.
W M Abd-Elhameed, Amr Kamel Amin, Abd-Elhameed Waleed Mohamed   +2 more
exaly   +2 more sources

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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
openaire   +1 more source

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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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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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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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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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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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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Probabilistic Bernoulli and Euler Polynomials

Russian Journal of Mathematical Physics
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Kim, T., Kim, D. S.
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Convolution and Reciprocity Formulas for Bernoulli Polynomials

Integers, 2011
AbstractWe prove a new convolution identity for sums of products of two Bernoulli polynomials. This can be rewritten to obtain a reciprocity relation for a related sum. The proof uses some results on Stirling numbers of both kinds which are of independent interest. In particular, a class of polynomials related to the Stirling numbers of the second kind
Takashi Agoh, Karl Dilcher
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