Results 211 to 220 of about 726,471 (254)

A hybrid method based on the orthogonal Bernoulli polynomials and radial basis functions for variable order fractional reaction-advection-diffusion equation

, 2021
In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is employed to define a new fractional version of 2D reaction-advection-diffusion equation.
M. Hosseininia, M. Heydari, Z. Avazzadeh, F. M. Maalek Ghaini   +3 more
semanticscholar   +1 more source

An Identity of Symmetry for the Bernoulli Polynomials

Discrete Mathematics, 2008
The author proves an identity of symmetry for the higher Bernoulli polynomials. It turns out implies that the recurrence relation and multiplication theorem for the Bernoulli polynomials discussed by \textit{F. T. Howard} [J. Number Theory 52, No. 1, 157--172 (1995; Zbl 0844.11019)], as well as a relation of symmetry between the power sum polynomials ...
Sheng-Liang Yang
exaly   +2 more sources

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

Numerical scheme for solving singular fractional partial integro‐differential equation via orthonormal Bernoulli polynomials

International journal of numerical modelling, 2019
In this paper, an efficient matrix method based on 2D orthonormal Bernoulli polynomials are developed to obtain numerical solution of weakly singular fractional partial integro‐differential equations (FPIDEs).
Nasrin Samadyar, Farshid Mirzaee
semanticscholar   +1 more source

Orthonormal Bernoulli polynomials collocation approach for solving stochastic Itô‐Volterra integral equations of Abel type

International journal of numerical modelling, 2019
In this paper, orthonormal Bernoulli collocation method has been developed to obtain the approximate solution of linear singular stochastic Itô‐Volterra integral equations.
Nasrin Samadyar, Farshid Mirzaee
semanticscholar   +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
openaire   +1 more source

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)}
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +2 more sources