- #1
*FaerieLight*
- 43
- 0
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
-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!
-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!