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    Taylor Series: open interval of convergence

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    The starting point for this problem is the representation of the natural exponential function by the corresponding Taylor series in powers of x:

    e^x= 1 + x +(1/2!)x^2 + (1/3!)x^3 + ......(1/n!)x^n + ........, x E R
    a) Let f(t) = e^(-t^2) , t E R. Define the Taylor series for f from the Taylor series for e^x.
    b) Let erf(x)= 2/ (square root of pi) times the integral from 0 to x e^(-t^2) dt.
    Determine the Taylor series for erf in powers of x. What is the open interval of convergence of
    the series?

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    Solution Summary

    We compute the Taylor series of two functions.