On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions

V. P. Motornyi

Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 591-620.

Résumé

We solve the problem of the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for the following classes of differentiable periodic functions: $W^r$ ($r>3$), $W^rH_\omega$ (where $\omega$ is a convex modulus of continuity and $r$ is odd), and $W^rL$ ($r=4,6,\dots$).

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