摘要：在连续性现实数量测不准的事实下，对现实数量大小及其关系的描述必须使用近似方法与进一步提高精度的近似方法。为此，对于函数也必须提出近似、全能近似、理想三种函数的技术术语．逐段具有足够阶连续导数的函数叫做好函数。为了解决某些难题，可以使用近似函数去替换原来的函数。

关键词：全能近似函数；δ函数；发散积分；海涅定理；奇异分布

中图分类号： 017 0174.22 029       文献标识码：A      文章编号：

Concept of Omnipotent Approximation Function and Its Applications

CAO Jun Yun¹, Cao Kai²

(1. Department of Mathematics and Information engineering, Henan Polytechnic University, Jiaozuo, 454000 PRC

 2. Department of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, 454000 PRC）

Abstract: On fact which the size of continuous actual quantity could not be measured exactly, for expression the size of continuous actual quantity and its relations must use the method of approximation and the method to raise exactness. So that must raise three technical terms of ideal function, approximation function and Omnipotent Approximation Function for to discuss function. The function which have sufficient order continuous derivative bit by bit is cold by good function.  For to settle some trouble questions, may use the approximation function to substitute its original function.  

Key words: omnipotent approximation function; δ-function; divergent integral; Heine’s theorem; strange distribution 

12全能近似函数的概念及其应用.doc

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