插值余项的大范围估计及其应用

A GLOBAL ESTIMATE AND APPLICATION FOR INTERPOLATING REMAINDER TERM

本文给出了代数插值余项中因子f^(q)(ξ_i)(q≥1)的全局性的可计算的上界函数,且是构造性的。特别,获得了Taylor 公式余项中因子f^(n+1)(ξ)的全局性的可计算的上界函数,从而解决了微分学中长期留下的f^(n+1)(ξ)的上界M 一般说不知是多大的难题。

In this paper,the Computable Superbound function of factor f(?)in algebraic interpolating re-mainder term is Constructed on space R(?).Particularly,the Computable superbound function of factorf^(n+1)(?)in remainder term of Taylor formula is given.Thus the difficult,long-term open problem indifferential Calculus,how large the superbound M of f^(n+1)(?)is,is solved.