In this paper we propose a modification of the exchange functional introduced by Perdew, Burke, and Ernzerhof, which significantly enlarges the original field of applications. This modification is obtained by a series expansion of the functional, which introduces one additional parameter, but retains all the asymptotic and scaling properties of the original model. The results obtained for structural, thermodynamic, kinetic, and spectroscopic properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parametrization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties makes the new exchange functional widely applicable, for both quantum chemistry and for condensed-matter physics.