Asymptotic expansions of complete Kähler-Einstein metrics with finite volume on quasi-projective manifolds

We give an elementary proof to the asymptotic expansion formula of Rochon and Zhang (2012) for the unique complete Kähler-Einstein metric of Cheng and Yau (1980), Kobayashi (1984), Tian and Yau (1987) and Bando (1990) on quasi-projective manifolds. The main tools are the solution formula for second-order ordinary differential equations (ODEs) with constant coefficients and spectral theory for the Laplacian operator on a closed manifold.