Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

in the course of trying to solve a rather complicated statistics problem, I stumbled upon a few difficult integrals. The most difficult looks like:

[tex] I(k,a,b,c) = \int_{-\infty}^{\infty} dx\, \frac{e^{i k x} e^{-\frac{x^2}{2}} x}{(a + 2 i x)(b+2 i x)(c+2 i x)} [/tex]

where [tex] a,b,c [/tex] are real positive numbers and [tex] k [/tex] is a real number. This integral cannot be done by simple contour integration because of the Gaussian factor. From the context, I expect error functions to appear in the solution.

Any clever ideas?

B.D.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Non-trivial Gaussian integral

**Physics Forums | Science Articles, Homework Help, Discussion**