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I'm reading a book at the moment in which the author states the identity:

[tex]\frac{1}{x-i\epsilon}=\frac{x}{x^2+\epsilon^2}+\frac{i\epsilon}{x^2+\epsilon^2} [/tex]

Which is fine, but then he goes on to state that this is equal to:

[tex] P\frac{1}{x}+i\pi\delta(x) [/tex]

Where P is the principal part. I think from googling the principle part means the sum of negative power terms in the Laurant expansion, yet I still have no clue as to how to get to this line.

Thanks for any help at all

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# What is the principal part in this identity?

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