  We propose a fast method for high order approximation of potentials of the
Helmholtz type operator Delta+kappa^2 over hyper-rectangles in R^n. By using
the basis functions introduced in the theory of approximate approximations, the
cubature of a potential is reduced to the quadrature of one-dimensional
integrals with separable integrands. Then a separated representation of the
density, combined with a suitable quadrature rule, leads to a tensor product
representation of the integral operator. Numerical tests show that these
formulas are accurate and provide approximations of order 6 up to dimension 100
and kappa^2=100.
