Geodesic
One property of best quadrature formulas
Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 551-562 
A. A. Zhensykbaev. One property of best quadrature formulas. Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 551-562. http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a6/
@article{MZM_1978_23_4_a6,
     author = {A. A. Zhensykbaev},
     title = {One property of best quadrature formulas},
     journal = {Matemati\v{c}eskie zametki},
     pages = {551--562},
     year = {1978},
     volume = {23},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is established that for class $W_p^r$ $(r=1,2,\dots;1\le p\le\infty)$ the best quadrature formulas of the form \begin{gather*} \int_0^1f(x)\,dx=\sum_{k=0}^\rho\sum_{i=1}^na_{ik}f^{(k)}(x_i)+R(f) \\ (0\le\rho\le r-1) \end{gather*} when $\rho=2m$ and $\rho=2m+1$ coincide with one another. This same fact also supervenes for the class $\widetilde{W}_p^r$ ($r=1,2,\dots$; $1\le p\le\infty$) of periodic functions.