# Questions tagged [cauchy-principal-value]

Computation of Cauchy principal values of integrals. May be tied in with contour integration, but should be separate from definite-integrals.

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### How to evaluate this by contour integral?

I want to evaluate cauchy principal value by complex contour integral, but I failed. Is this integral solved by contour integral? $$PV\int_0^\infty\frac{1}{x^3-1}\,\mathrm{d}x$$
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### Motivation behind Cauchy principal value of an improper integral? [duplicate]

According to the Wikipedia, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined. The ...
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### Asymptotic behavior of a 2D integral: retarded/advanced green's function with saddle point dispersions

I want to analytically evaluate the 2D integral for some real $E< 1$ $I^\pm(E)=\lim_{\eta \rightarrow 0}\int_{-1}^{1} dx dy \frac{1}{E\pm i\eta -xy}$ In particular, I want to understand the ...
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### Finding the Cauchy Principal Value of $\int_{-\infty}^{\infty}\frac{1}{x-i}dx$

I know that the Cauchy Principal value of $\int_{-\infty}^{\infty}\frac{1}{x-i}dx=i\pi$ but I do not understand how to get to this. I understand how to use the principal value for functions with real ...
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