Resolution of the Plane-symmetric Einstein-Maxwell fields with a generalization of the Lambert W function

Abstract

Abstract Here, the Einstein-Maxwell field equation with plane-symmetry is resolved and a solution involving a generalized Lambert W function is obtained. This generalized Lambert W function is studied and its derivative, Taylor series, Mellin transform and approximation formula are derived and its real branches are determined. Implications of these analytic properties to the solution function are also presented.