积分的超渐近展开与Stokes不连续性的光滑化

Hyperasymptotics for Integral and Smoothings for Stokes' Discontinuity

渐近分析中的经典最速下降法近十年来出现的重要新发展——超渐近展开 ,使人们对于历史上著名的 Stokes现象实质有了更深刻的认识。然而 ,有关这方面的资料却各自独立且不易读懂 ,尤其缺少思路清晰的综述。本文力求通俗自然概括整理出其中的主要成果 ,有些地方不得不根据作者的理解作了改动与补充 。

In recent 10 years,hyperasymptotic expansion-the new and important development in the classic steepest descents among the asymptotic analysis arises,it makes us to understand the essence of famous stokes phenomenon in history deeply.The materials involved are seperate and not readable,and especially lack of clear summary.In this paper,main achievements about the expansion are given popularly and naturally,some individual changes and supplements are made by the auther.