摘要
推导了复变函数一个广义意义上的泰勒级数表达式 ,证明了有关的收敛性定理 ,大大增大摄动级数解的收敛区域· 定理的证明亦为一种新的、求解非线性问题的解析方法 (即“同伦分析方法”)的有效性奠定了一个坚实的数理逻辑基础·
A generalized Taylor series of a complex function was derived and some related theorems about its convergence region were given. The generalized Taylor theorem can be applied to greatly enlarge convergence regions of approximation series given by other traditional techniques. The rigorous proof of the generalized Taylor theorem also provides us with a rational base of the validity of a new kind of powerful analytic technique for nonlinear problems, namely the homotopy analysis method.
出处
《应用数学和力学》
CSCD
北大核心
2003年第1期47-54,共8页
Applied Mathematics and Mechanics
基金
国家杰出青年基金资助项目 (5 0 12 5 92 3)
