Geodesic
Estimate of the remainder of a cubature formula for a hypersphere
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 627-632 Cet article a éte moissonné depuis la source Math-Net.Ru

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An estimate is given for the remainder term of a cubature formula of special type for calculating an integral over an $n$-dimensional sphere. The algebraic degree of precision of the formula is the highest among formulas of this type and is equal to $4p-1$. Appearing in the estimate is an upper bound of the absolute values of all the partial derivatives of the integrand function of order $4p$ in the domain of integration. 
@article{MZM_1969_6_5_a13,
     author = {I. P. Mysovskikh},
     title = {Estimate of the remainder of a~cubature formula for a~hypersphere},
     journal = {Matemati\v{c}eskie zametki},
     pages = {627--632},
     year = {1969},
     volume = {6},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a13/}
}
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I. P. Mysovskikh. Estimate of the remainder of a cubature formula for a hypersphere. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 627-632. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a13/