There is the identity(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Homework Help: Using an identity

Can you offer guidance or do you also need help?

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