# Taylor Series: open interval of convergence

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?

https://brainmass.com/math/real-analysis/taylor-series-open-interval-convergence-527467

#### Solution Summary

We compute the Taylor series of two functions.

$2.19