On optimal interval quadrature formulae on classes of differentiable periodic functions

V.F. Babenko; D.S. Skorokhodov

doi:10.15421/240703

On optimal interval quadrature formulae on classes of differentiable periodic functions

V.F. Babenko (Dnipropetrovsk National University, Institute of Applied Mathematics and Mechanics of NAS of Ukraine), https://orcid.org/0000-0001-6677-1914
D.S. Skorokhodov (Dnipropetrovsk National University), https://orcid.org/0000-0001-8494-5885

Abstract

We solved the problem about the best interval quadrature formula on the class $$$W^r F$$$ of differentiable periodic functions with arbitrary permutation-invariant set $$$F$$$ of derivatives of order $$$r$$$. We proved that the formula with equal coefficients and $$$n$$$ node intervals, which have equidistant middle points, is the best on given class.

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