Series expansion of an integral at infinity

by Irid
Tags: expansion, infinity, integral, series
Irid is online now
Oct5-13, 11:48 AM
P: 208
I'm fiddling with Wolfram Alpha and I can't find a definition of what do they mean by the "Series expansion of the integral at x -> inf". In particular, I have two divergent integrals and I am wondering whether their ratio is some finite number. Here it is:

[itex] \left[\int_0^{\infty} \frac{1}{x^n}e^{1/x}\, dx \right] \left[\int_{-\infty}^{+\infty}e^{u^2} \cos u\, du \right]^{-1}[/itex]

where n is a parameter. Based on wolfram's suggestion, I think that if n=2, the above expression converges to something meaningful, since both integrals apparently have the series expansion at infinity as exp(x^2).
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