# Math Help - Taylor Series of the Error Function

1. ## Taylor Series of the Error Function

Problem:
$erf(x)=\frac{1}{\sqrt{\pi}}\int^0_x e^{-t^2/2} dt$
Find the Taylor series of the error function from the Taylor series of $f(r)=e^r$ (set $r=-t^2/2$ and integrate)

I tried to start this problem by writing out the Taylor series for $f(r)=e^r$ as suggested, but I do not know how I am supposed to proceed from here. Any advice would be much appreciated.

2. Originally Posted by LithiumPython
Problem:
$erf(x)=\frac{1}{\sqrt{\pi}}\int^0_x e^{-t^2/2} dt$
Find the Taylor series of the error function from the Taylor series of $f(r)=e^r$ (set $r=-t^2/2$ and integrate)

I tried to start this problem by writing out the Taylor series for $f(r)=e^r$ as suggested, but I do not know how I am supposed to proceed from here. Any advice would be much appreciated.
Try replacing $r$ with $-\frac{t^2}{2}$...