Matematičeskie zametki, Tome 6 (1969) no. 4, pp. 475-481
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N. E. Lushpai. Best quadrature formulas on classes of differentiable periodic functions. Matematičeskie zametki, Tome 6 (1969) no. 4, pp. 475-481. http://geodesic.mathdoc.fr/item/MZM_1969_6_4_a12/
@article{MZM_1969_6_4_a12,
author = {N. E. Lushpai},
title = {Best quadrature formulas on classes of differentiable periodic functions},
journal = {Matemati\v{c}eskie zametki},
pages = {475--481},
year = {1969},
volume = {6},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_4_a12/}
}
TY - JOUR
AU - N. E. Lushpai
TI - Best quadrature formulas on classes of differentiable periodic functions
JO - Matematičeskie zametki
PY - 1969
SP - 475
EP - 481
VL - 6
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1969_6_4_a12/
LA - ru
ID - MZM_1969_6_4_a12
ER -
%0 Journal Article
%A N. E. Lushpai
%T Best quadrature formulas on classes of differentiable periodic functions
%J Matematičeskie zametki
%D 1969
%P 475-481
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1969_6_4_a12/
%G ru
%F MZM_1969_6_4_a12
A solution is given to the problem of finding the best quadrature formula among formulas of the form $$ \int_0^{2\pi}f(x)\,dx\approx\sum_{k=0}^{m-1}\sum_{l=0}^\rho p_{k,l}f^{(l)}(x_k) $$ which are exact in the case of a constant, for $\rho=r-1$, $r=1,2,3,\dots$ and $\rho=r-2$, $r$ even, for the classes $W^{(r)}L_qM$ of $2\pi$-periodic functions.
