Geodesic
Formulas for the approximate calculation of integrals over the whole plane
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 466-470 
A. K. Ponomarenko. Formulas for the approximate calculation of integrals over the whole plane. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 466-470. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/
@article{ZVMMF_1990_30_3_a11,
     author = {A. K. Ponomarenko},
     title = {Formulas for the approximate calculation of integrals over the whole plane},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {466--470},
     year = {1990},
     volume = {30},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/}
}
TY  - JOUR
AU  - A. K. Ponomarenko
TI  - Formulas for the approximate calculation of integrals over the whole plane
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 466
EP  - 470
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/
LA  - ru
ID  - ZVMMF_1990_30_3_a11
ER  - 
%0 Journal Article
%A A. K. Ponomarenko
%T Formulas for the approximate calculation of integrals over the whole plane
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 466-470
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/
%G ru
%F ZVMMF_1990_30_3_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

Cubature formulas with $4s+1$ and $4s-1$ nodes, which have the $(4s-1)$ property and $(4s-3)$ property, respectively, are constructed for the approximate evaluation of an integral over a plane. The nodes of the formulas are common zeros of certain orthogonal polynomials.

[1] Mysovskikh I. P., Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | MR

[2] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

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

[4] Mysovskikh I. P., “Primenenie ortogonalnykh mnogochlenov k postroeniyu kubaturnykh formul”, Zh. vychisl. matem. i matem. fiz., 12:2 (1972), 467–475 | Zbl

[5] Radon J., “Zur mechanischen Kubatur”, Monatsh. Math., 52:4 (1948), 286–300 | DOI | MR

[6] Ponomarenko A. K., “Nekotorye kubaturnye formuly dlya ploskosti, soderzhaschie proizvodnye”, Metody vychislenii, 14, Izd-vo LGU, L., 1985, 24–35 | MR