Comment on A note on generalized radial mesh generation for plasma electronic structure

In a recent note, B.G. Wilson and V. Sonnad [1] proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h[alpha] using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we propose a direct proof of that equation. (C) 2011 Elsevier B.V. All rights reserved.