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Principle Value

  1. Oct 4, 2007 #1
    My professor wrote on the board,
    [tex]\lim_{\eta \rightarrow 0^+} \frac{1}{x-i \eta} = P(\frac{1}{x}) + i \pi \delta(x)[/tex]
    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?
    Last edited: Oct 4, 2007
  2. jcsd
  3. Oct 5, 2007 #2


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    ??Well, obviously 1/x does have a singularity at x= 0!
  4. Oct 5, 2007 #3
    So what does P(1/x) mean? I understand what
    [tex]P\int_{-\inf}^{\inf}\frac{1}{x} dx[/tex]
    means. When I saw principle value defined, it was operating on an integral that has a singularity. What does it mean for it to operate on a function with a singularity?
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