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I am working on a question that involves finding the Taylor expansion of the error function. The question is stated as follows

The error function is defined by $\mathrm{erf}(x):=\frac {2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^{2}}dt$. Find its Taylor expansion.

I know that the Taylor series of the function $f$ at $a$ is given by

$$f(x)=\sum_{n=0}^{\infty}\frac {f^{(n)}(a)}{n!}(x-a)^{n}.$$

However, the question doesn't give a point $a$ with which to center the Taylor series. How should I interpret this? May I use a Maclaurin series, with $a=0$? This appears to be what was done on the Wikipedia page here: http://en.wikipedia.org/wiki/Error_function

Any explanations and advice would be appreciated.

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    $a=0$ seems OK for me. I would expand $e^{-t^2}$ in a power series and integrate term by term.2012-03-28

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