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    Analytic Approximation for an Oscillatory Integral

    The integral I am trying to solve is a version of a Fourier transform, so it would be better if the approximation were r-dependent. I was thinking that integrating by parts twice would sharpen the 1/√(...) piece and make it look like a delta-function. Then the integration would be easy if I...
  2. C

    Analytic Approximation for an Oscillatory Integral

    I'm looking for a way to write down an analytic approximation for the following integral: \int_0^\infty \frac{k \sin(kr)}{\sqrt{1+v^2(k-k_F)^2}}dk Let's assume that v kF >> 1, so that the the oscillating piece at large k doesn't contribute much uncertainty. Ideas? Thus far, Mathematica has...
  3. C

    Fundamental theorem of calculus for double integral

    Jhenrique, what the others aren't bothering to tell you is that your hypothesis is following the right line of intuition. The correct generalization of the fundamental theorem of Calculus to a two-dimensional integration across a rectangular region is given by \iint \limits_{y_0 x_0}^{y_1...
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