Corrected Euler-Maclaurin’s formulae
Copyright policy )Corrected Euler-Maclaurin’s formulae
The aim of this paper is to derive corrected Euler-Maclaurin's formulae, i.e. open type quadrature formulae where the integral is approximated not only with the values of the function in points (5a+b)/6, (a+b)/2 and (a+5b)/6, but also with values of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than the standard Euler-Maclaurin's formulae. Using the derived formulae, a number of inequalities for various classes of functions are obtained.
- University of Zagreb Croatia
open type quadrature formulae; corrected Maclaurin's formula; Bernoulli polynomials; functions of bounded variation; Lipschitzian functions, corrected Maclaurin's formula, Bernoulli polynomials, Lipschitzian functions, Numerical quadrature and cubature formulas, Open type quadrature formulae, open type quadrature formulae, Euler-Maclaurin formula in numerical analysis, functions of bounded variation, Inequalities for sums, series and integrals, Corrected Maclaurin's formulae, Functions of bounded variation
open type quadrature formulae; corrected Maclaurin's formula; Bernoulli polynomials; functions of bounded variation; Lipschitzian functions, corrected Maclaurin's formula, Bernoulli polynomials, Lipschitzian functions, Numerical quadrature and cubature formulas, Open type quadrature formulae, open type quadrature formulae, Euler-Maclaurin formula in numerical analysis, functions of bounded variation, Inequalities for sums, series and integrals, Corrected Maclaurin's formulae, Functions of bounded variation
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!