Taylor Series of the Error Function

**LithiumPython** · February 15th 2010, 04:28 PM

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.

**Prove It** · February 15th 2010, 04:29 PM

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 $-\frac{t^2}{2}$ ...

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