ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (1): 53-60.

ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD

廖世俊

School of Naval Architecture & Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, China

收稿日期:2002-01-28 修回日期:2002-10-15 出版日期:2003-01-18 发布日期:2003-01-18
基金资助:
the National Science Fund for Distinguished Young Scholars of China (50125923)

ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD

LIAO Shi-jun

School of Naval Architecture & Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, China

Received:2002-01-28 Revised:2002-10-15 Online:2003-01-18 Published:2003-01-18
Supported by:
the National Science Fund for Distinguished Young Scholars of China (50125923)

摘要/Abstract

摘要： 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.

中图分类号:

廖世俊. ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 53-60.

LIAO Shi-jun. ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 53-60.

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ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD

ON A GENERALIZED TAYLOR THEOREM: A RATIONAL PROOF OF THE VALIDITY OF THE HOMOTOPY ANALYSIS METHOD

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