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using some or all of a lattice of 9 or 16 points equally spaced over the square. In this note, the restriction to equal spacing is relaxed, to allow points to be chosen to give greater accuracy in the approximation to the integral. The restriction to two dimensions or variables is also removed in some cases. It is still assumed that the integrand f(xx, x2, ■ ■ • , xn) may be expanded in a power series as far as we please in all variables—in other words, that for the precision desired, the integrand may be replaced by a polynomial of suitable degree. Considerations of symmetry once again ensure that we need concern ourselves only with terms of even degree in each variable separately. By scale changes we also make the range of integration — h to +h in each variable.

Numerical quadrature over a rectangular domain in two or more dimensions. III. Quadrature of a harmonic integrand