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Euler Polynomials and the Related Quadrature Rule
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Gabriella Bretti
Published/Copyright:
February 24, 2010
Abstract
The use of Euler polynomials and Euler numbers allows us to construct a quadrature rule similar to the well-known Euler–MacLaurin quadrature formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term and numerical examples are also given.
Key words and phrases.: Euler polynomials; Euler numbers; Euler–MacLaurin quadrature formula; quadrature rules
Received: 2001-03-10
Published Online: 2010-02-24
Published in Print: 2001-September
© Heldermann Verlag
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Keywords for this article
Euler polynomials;
Euler numbers;
Euler–MacLaurin quadrature formula;
quadrature rules
Articles in the same Issue
- A New Method of Solving the Basic Plane Boundary Value Problems of Statics of the Elastic Mixture Theory
- Euler Polynomials and the Related Quadrature Rule
- MD-Numbers and Asymptotic MD-Numbers of Operators
- Boundary Variational Inequality Approach in the Anisotropic Elasticity for the Signorini Problem
- On Vector Sums of Measure Zero Sets
- Hyper-Holomorphic Cells and Fredholm Theory
- On a Representation of the Derivative of a Conformal Mapping
- On a Trace Inequality for One-Sided Potentials and Applications to the Solvability of Nonlinear Integral Equations
- Quasiconformal Deformations of Holomorphic Functions
- Convolutional Codes and Frequency Responses
- Boundary Integral Equations of Plane Elasticity in Domains with Peaks
- Pluriregular, Plurigeneralized Regular Equations in Clifford Analysis
- On Volterra Type Singular Integral Equations
