Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

Abstract

We review the exact solutions of several transcendental equations, obtained by Siewert and his co-workers, in the '70s. Some of them are expressed in terms of the generalized Lambert functions, recently studied by Mezö, Baricz and Mugnaini. For some others, precise analytical approximations are obtained. In two cases, the asymptotic form of Siewert's solutions are written as Wright omega functions.

17 pages, 5 figures

References in corpus (2)

• Generalization of Lambert $W$ function, Bessel polynomials and transcendental equations
• The Langevin function and truncated exponential distributions