[[급수,series]] 중 [[테일러_급수,Taylor_series]]에서 0을 xxxxx에 대입한 결과이다, 혹은 xxxxx가 0인 경우이다, ....

$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n$
i.e.
$f(x)=\frac{f(0)}{0!}x^0+\frac{f^{\prime}(0)}{1!}x^1+\frac{f^{\prime\prime}(0)}{2!}x^2+\;\cdots$
i.e.
$f(x)=f(0)+f^{\prime}(0)x+\frac{f^{\prime\prime}(0)}{2!}x^2+\frac{f^{(3)}(0)}{3!}x^3+\;\cdots\;+\frac{f^{(n)}(0)}{n!}x^n+\;\cdots$


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||Taylor 급수 ||Maclaurin 급수 ||
||$\sum_{n=0}^{\infty}{\frac{f^{(n)}(x_{0})}{n!}(x-x_{0})^{n}}$ ||$\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n$ ||

http://mathworld.wolfram.com/MaclaurinSeries.html