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  1. R

    Integral from 0 to ∞ with singularity at x=0

    Here's an integral that is currently giving me grey hairs: \int_0^{\infty} \frac{1}{x} \exp(i \frac{k}{x}(a-c \cos(\theta + wx))) dx I've tried different approaches like contour integration around x=0 and replacing the exponential by its Taylor sum to have: \int_0^{\infty}...
  2. R

    Approximation of error function-type integral

    Hi! How do I approximate the integral \begin{equation} \int_0^{\infty} dt \:e^{-iA(t-B)^2} \end{equation} with A, B real, A > 0, and B=b \cos\theta where 0 \leq \theta < 2\pi? I guess for B\ll 0 the lower limit may be extended to - \infty to yield a full complex gaussian integral, but what...
  3. R

    Green's function for Klein-Gordon equation in x-space

    I'm trying to derive the x-space result for the Green's function for the Klein-Gordon equation, but my complex analysis skills seems to be insufficient. The result should be: \begin{eqnarray} G_F(x,x') = \lim_{\epsilon \rightarrow 0} \frac{1}{(2 \pi)^4} \int...