Abstract
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.
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I. P. Mysovskikh, “Cubature formulas for evaluating integrals over a hypersphere,” Dokl. Akad. Nauk SSSR,147, No. 3, 552–555 (1962).
L. V. Kantorovich, “On special methods for numerically integrating even and odd functions,” Trudy Matem. in-ta Akad. Nauk SSSR,28, 3–25 (1949).
V. K. Dzyadyk and V. A. Panasovich, “On an estimate of the remainder for some cubature formulas,” Ukrainsk. Matem. Zh.,20, No. 2, 147–155 (1968).
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Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 627–632, November, 1969.
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Mysovskikh, I.P. Estimate of the remainder of a cubature formula for a hypersphere. Mathematical Notes of the Academy of Sciences of the USSR 6, 839–842 (1969). https://doi.org/10.1007/BF01101414
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DOI: https://doi.org/10.1007/BF01101414