Estimate of the remainder of a cubature formula for a hypersphere

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.Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 627–632, November, 1969.