节点文献
分段点处高阶导数存在性的直接判别法
Criteria for the Existence of Higher Derivatives of Piecewise Functions
【摘要】 利用泰勒展开式,把分段函数在以x0为分段点的相邻区间上展开为(x-x0)的泰勒级数,然后通过观察和比较相邻分段区间上泰勒展开式中的k阶系数是否对应相等,来判断分段函数在x=x0点是否存在k阶导数.
【Abstract】 Using Taylor expansion,a piecewise-defined function can be expanded as power series of(x-x0) in a neighborhood of x0,one for x>x0 and the other for x<x0.By comparing the corresponding Taylor coefficients we can establish criteria for the existence of higher derivatives of the function at x=x0.
- 【文献出处】 高等数学研究 ,Studies in College Mathematics , 编辑部邮箱 ,2012年01期
- 【分类号】O172.1
- 【下载频次】157