Geodesic
Best quadrature formula for some classes of periodic differentiable functions
Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1055-1071.

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In this work there is solved the problem of the best quadrature formula of the form $$ \int_0^1f(x)\,dx=\sum_{i=1}^na_if(x_i)+R(f) $$ on the classes of periodic functions $W^r_p$ ($r=1,2,\dots$; $1\leqslant p\leqslant\infty$). Bibliography: 13 titles. 
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A. A. Zhensykbaev. Best quadrature formula for some classes of periodic differentiable functions. Izvestiya. Mathematics , Tome 11 (1977) no. 5, pp. 1055-1071. http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a7/

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[2] Lushpai N. E., “Ob odnoi optimalnoi kvadrature dlya klassa differentsiruemykh periodicheskikh funktsii”, Izv. vuzov, matem., 1973, no. 4(131), 55–63 | MR | Zbl

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[7] Nikolskii S. M., Kvadraturnye formuly, Nauka, M., 1974 | MR

[8] Zhensykbaev A. A., “Priblizhenie nekotorykh klassov differentsiruemykh periodicheskikh funktsii interpolyatsionnymi splainami po ravnomernomu razbieniyu”, Matem. zametki, 15:6 (1974), 955–966 | Zbl

[9] Zhensykbaev A. A., “Tochnye otsenki ravnomernogo priblizheniya nepreryvnykh periodicheskikh funktsii splainami $r$-go poryadka”, Matem. zametki, 13:2 (1973), 217–228 | Zbl

[10] Krylov V. I., Priblizhennoe vychislenie integralov, Nauka, M., 1967 | MR

[11] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[12] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR

[13] Zhensykbaev A. A., “O nailuchshei kvadraturnoi formule na klasse $W^r L_p$”, Dokl. AN SSSR, 227:2 (1976), 277–279 | MR | Zbl