The sound field produced by plane baffled transducers of highkacan be described by treating the radiated space as a waveguide of infinite size. Under the Fresnel approximation for cylindrical geometries, the modes of this waveguide are known to be the Gaussian–Laguerre functions. The general Gaussian–Laguerre formulation for expanding acoustic fields is presented and numerical results are shown for the circular piston. The Gaussian–Laguerre expansion coefficients for this example are obtained analytically, thus providing a new solution in series form.