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My professor wrote on the board,
\lim_{\eta \rightarrow 0^+} \frac{1}{x-i \eta} = P(\frac{1}{x}) + i \pi \delta(x)
where P stands for principle value. I understand how the imaginary part comes about but why do you need P for the real part. Plus I thought Principle Value is defined for integrals that have singularities in them. Did he make an error when he wrote this?
thanks
\lim_{\eta \rightarrow 0^+} \frac{1}{x-i \eta} = P(\frac{1}{x}) + i \pi \delta(x)
where P stands for principle value. I understand how the imaginary part comes about but why do you need P for the real part. Plus I thought Principle Value is defined for integrals that have singularities in them. Did he make an error when he wrote this?
thanks
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