Rational solutions of the Toda lattice equation in Casoratian form

A recursive procedure is presented for constructing rational solutions to the Toda lattice equation through the Casoratian formulation. It allows us to compute a broad class of rational solutions directly, without computing long wave limits in soliton solutions. All rational solutions arising from the Taylor expansions of the generating functions of soliton solutions are special ones of the general class, but only a Taylor expansion containing even or odd powers leads to non-constant rational solutions. A few rational solutions of lower order are worked out.