# Taylor Series of the Error Function

• Feb 15th 2010, 04:28 PM
LithiumPython
Taylor Series of the Error Function
Problem:
$\displaystyle erf(x)=\frac{1}{\sqrt{\pi}}\int^0_x e^{-t^2/2} dt$
Find the Taylor series of the error function from the Taylor series of $\displaystyle f(r)=e^r$ (set $\displaystyle r=-t^2/2$ and integrate)

I tried to start this problem by writing out the Taylor series for $\displaystyle f(r)=e^r$ as suggested, but I do not know how I am supposed to proceed from here. Any advice would be much appreciated.
• Feb 15th 2010, 04:29 PM
Prove It
Quote:

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

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

Try replacing $\displaystyle r$ with $\displaystyle -\frac{t^2}{2}$...