A one‐way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy‐absorbing numerical boundary conditions. The design of a one‐way wave equation is connected with the approximation of (1−s 2)1 / 2 on [−1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L 2, L ∞, and other alternative classes of approximants that have better wide‐angle behavior. For theoretical results establishing the well posedness of these wide‐angle equations, see the work of Trefethen and Halpern [‘‘Well‐posedness of one‐way wave equations and absorbing boundary conditions,’’ Math. Comput. 4 7, 421–435 (1986)].