Cubature weight formulae of highest algebraic accuracy (Q1311594)

Using some known results about cubature formulae for trigonometric polynomials the author presents a method for constructing cubature formulae with the weight \(w(x_ 1, \dots, x_ n) = \prod^ n_{i = 1} (1 - x_ i^ 2)^{-1/2}\), which integrate exactly all algebraic polynomials of degree \(m\). In case \(m=2\) and \(m=3\) the resulting cubature formulae are of highest algebraic degree of precision.