asymptotic expansion of the integral for large tau

Asked Aug 14 '14 at 23:04

Active Aug 16 '14 at 17:09

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How can I proceed to resolve this integral?

$$ c_1\int_{-\infty}^{\infty}{\frac{\cos\left(x\tau\right)}{\left(1 + c_{2}\,x\right)^{\alpha}}}\, \,{\rm d}x $$ where $c_1, c_2$ are positive constants, and $\alpha \in \Bbb R$. and what is the asymptotic expansion of the integral for large $\tau$. Thank you.

edited Aug 16 '14 at 17:09

asked Aug 14 '14 at 23:04

Ahmed Abrous

Have a look to the accepted answer of: http://math.stackexchange.com/questions/895436/integral-of-the-von-karman-equation (second addendum) – Dmoreno Aug 14 '14 at 23:24
@Dmoreno It is the same OP that accepted it. I am not sure if you (OP) was not sure about the answer? :/ – Chinny84 Aug 14 '14 at 23:30
Oh, I see it now. Maybe he's looking for a more detailed explanation. He should show us, by the way, what his efforts on the resolution of the problem are. – Dmoreno Aug 14 '14 at 23:37
I am searching an explanation or a way to resolve the problem :) and not a result. – Ahmed Abrous Aug 14 '14 at 23:44
Is it ok like that :) ? – Ahmed Abrous Aug 14 '14 at 23:48
No because at first, the equation is not even and after that I have not found the table which gives the usual integral. So It takes work to get the good way to resolve this integral. – Ahmed Abrous Aug 14 '14 at 23:51
I have done the change of variable $t=1+c2*x$ after that I have used the Mellin Transform, but the result is not the expected one. – Ahmed Abrous Aug 14 '14 at 23:56
My bad! I totally misread the integral! Sorry – Chinny84 Aug 15 '14 at 00:05
What is $\tau$? (Constant, Variable etc) – Display Name Aug 15 '14 at 09:05
$\tau$ can be considered as a constant for integration. – Ahmed Abrous Aug 15 '14 at 15:01
I just evaluated something similar. – Felix Marin Aug 16 '14 at 03:48

asymptotic expansion of the integral for large tau

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