  We give an elementary proof to the asymptotic expansion formula of
Rochon-Zhang for the unique complete K\"ahler-Einstein metric of Cheng-Yau,
Kobayashi, Tian-Yau and Bando on quasi-projective manifolds. The main tools are
the solution formula for second order ODE's with constant coefficients and
spectral theory for Laplacian operator on a closed manifold.
