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Homework Help: Using an identity

  1. Jan 7, 2010 #1
    There is the identity

    [tex] \dfrac{1}{1-x+i0} = PV \dfrac{1}{x} - i \pi \delta(1-x) [/tex]

    PV corresponds to Cauchy principal value.

    But how can I handle a term like

    [tex] \dfrac{1}{(x-i0)(1-x+i0)} [/tex]

    and how can I use the identity above? I tried several things such as writing

    [tex] \dfrac{1}{(x-i0)(1-x+i0)} = \dfrac{1}{x(1-x) + i (x-1) 0} = PV \dfrac{1}{x(1-x)} - i \pi \delta(x(1-x)) \text{signum}(x-1) [/tex]

    But I don't know to handle this term correctly. Could anyone help me please?
  2. jcsd
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