I'm not exactly sure that what I want to do is an asymptotic expansion, but basically I would like to find a power series approximation in s of(adsbygoogle = window.adsbygoogle || []).push({});

-s [itex]\int[/itex] [itex]\frac{e^{-x^{2}}}{x-s}[/itex] dx

for large values of s.

The integral is meant to be from -∞ to +∞.

I can see that for large s, the denominator becomes approximately -s, and this cancels with the -s out the front of the integral, so that the whole thing is approximately equal to [itex]\sqrt{\pi}[/itex], but this is too much of an approximation. I would like to have some 'error' terms in there as well, after the [itex]\sqrt{\pi}[/itex], except I can't seem to get the right ones using Taylor expansions. Should I be looking to do asymptotic expansions instead? Or is there a way to do it with just power series?

Thanks a lot!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Asymptotic Expansion of an Integral

**Physics Forums | Science Articles, Homework Help, Discussion**