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Math Help - Taylor Series of the Error Function

  1. #1
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    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.
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    Quote Originally Posted by LithiumPython View Post
    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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