Highly accurate approximations of Green's and Neumann functions on rectangular domains

Green's and Neumann functions of -Delta, where Delta is the Laplacian opera tor, on a rectangular domain are approximated to any desired degree of accu racy by finite series. Many applications require only a modest number of te rms. Upper bounds for the errors in these approximations are also derived. The approximating functions reveal the structural similarities and differen ces in Green's and Neumann functions.