# Definition of asymptotic relation

by hanson
Tags: asymptotic, definition, relation
 P: 320 Hi all! Can anyone explain to me why the asymptotic relation between a function and a power series is defined in such a way: For all N, $$f(x) - \sum_{n=0}^N a_n(x-x_0)^n << (x-x_0)^N$$ How does this incorporate the idea of asymptoticity? Please kindly help.
 Quote by hanson Hi all! Can anyone explain to me why the asymptotic relation between a function and a power series is defined in such a way: For all N, $$f(x) - \sum_{n=0}^N a_n(x-x_0)^n << (x-x_{0})^{N}$$ How does this incorporate the idea of asymptoticity? Please kindly help.
$$\lim_{x\to{x}_{0}}\frac{f(x) - \sum_{n=0}^N a_n(x-x_0)^n}{(x-x_{0})^{N}}=0$$