The integrands in the dispersion equation are not integrable in general , so we used the asymptotic expansion solution to analyze the behavior of the dispersion relation at the singularity and mapped the dispersion relation curves approximately the system composed of collisionless particles which obey maxwellian distribution or all kinds of degenerate distribution , even in their mixture system , their dispersion relation are analogous 一般來說,色散方程中的被積函數(shù)都是難以求積的,本文是用函數(shù)逼近法分析色散方程在奇點處的行為,并大致劃出色散關系曲線。由無碰撞粒子組成的系統(tǒng),不管初始分布是maxwell分布還是各種簡并分布,甚至是這些分布的混合體,色散關系都是相似的。