In applications, the main role play analytic solutions that are expressible by the convergent power series expanded around some initial point. Typically the expansion point is ξ ξ = 0 , which is also a singular point (fixed singularity) of the equation, and there is provided some initial data θ θ ( 0 ) at the centre of the star. One can prove that the equation has the convergent power series/analytic solution around the origin of the form θ θ ( ξ ξ ) = θ θ ( 0 ) − − θ θ ( 0 ) n 6 ξ ξ 2 + O ( ξ ξ 3 ) , ξ ξ ≈ ≈ 0.