An extension of the Euler-Maclaurin quadrature formula using a parametric type of Bernoulli polynomials

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Abstract

In this paper, we introduce a parametric type of Bernoulli polynomials and study their basic properties in order to establish an extension of Euler-Maclaurin quadrature rules and compare them with the well-known ordinary case.

MSC

11B68
11Y35
11C08

Keywords

Euler-Maclaurin quadrature rules
Bernoulli polynomials and numbers
Appell polynomials
Generating functions
Fourier expansions

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