Transformations of the Equation of Equilibrium for Isothermal Plane-Symmetric Configuration

We have discussed a few transformations which connect solutions of the isothermal equation (analogue of the Lane-Emden equation (LEE)) for plane-symmetric configuration in (μ_ρ; ν_ρ); (μ_p; ν_p); (μ_ψ; ν_ψ) planes and (y_ρ; z_ρ); (y_p; z_p); (y_ψ; z_ψ) planes. Approximate analytical solutions for (μ_ψ; ν_ψ) planes are tabulated following the technique of Pade′ approximants. Physical aspects of the problem and interpretations of the results have also been included.