基於 Charles 以及 Berman, Berndtsson 和 Sj\"{o}strand 的論文，我們展示了一個在$L^k$上 Bergman kernel 漸近展開式的證明，其中$L$是緊緻的凱勒流形上的正線叢。最後我們給出了在複射影空間上的 Bergman kernel 漸進展開式的詳細計算。;We present a proof of an asymptotic expansion in power of $k$ on the Bergman kernel to $L^k$, where $L$ is a positive line bundle over a compact K\"{a}hler manifold, based on the papers of Charles and Berman, Berndtsson and Sj\"{o}strand. We give an explicit computation of the Bergman kernel on complex projective spaces.
