The well‐known low‐frequency expansion of the total acoustic field in the exterior of a penetrable spherical scatterer is revisited in view of the Atkinson Wilcox theorem. The corresponding low‐frequency approximations of any order are calculated following a purely algebraic algorithmic procedure, based on the spectral decomposition of the problem's far field pattern. As an indication of its accuracy and effectiveness, the proposed algebraic procedure is shown to recover already known low‐frequency coefficients and also to deduce higher order of approximations. The proposed track of calculations leads to a closed‐form expression of any such coefficient and has been recently applied on impenetrable spherical scatterers as well, offering equally accurate results. The effectiveness of the proposed procedure indicates an underlying general efficient method applicable to a wider class of starshaped scatterers. Copyright © 2016 John Wiley & Sons, Ltd.