I'm looking for a way to write down an analytic approximation for the following integral:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_0^\infty \frac{k \sin(kr)}{\sqrt{1+v^2(k-k_F)^2}}dk[/tex]

Let's assume that v k_{F}>> 1, so that the the oscillating piece at large k doesn't contribute much uncertainty. Ideas? Thus far, Mathematica has failed me, though I have been able to generate some numerical solutions. Is there some way to take advantage of the fact that the integrand is peaked at k_{F}?

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# Analytic Approximation for an Oscillatory Integral

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