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>> No.12516463 [View]
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12516463

>>12516449
Rewriting the cosign as exp too, the resulting inner integral
[math]\int e^{\pm i(x_0\pm x)k}{\mathrm e}^{-ck^2}{\mathrm d}k[/math]
can maybe be approached with some from this list.

https://en.wikipedia.org/wiki/Common_integrals_in_quantum_field_theory

You might up with a second Gaussian integral that you tackle in the same fashion.

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