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Integration with branch cuts

  1. Apr 22, 2009 #1
    Hi,

    I find integration with branch cuts difficult to grasp.
    For example, I can understand that [tex]\sqrt{x}[/tex] is mutivalued and has 2 branches if we take a branch cut from 0 to +infty. But given it to be integrated from -infty to +infty what is the the meaning of taking a branch of [tex]\sqrt{x}[/tex] ?

    Could u pls give me some pointers to look or guide me with this example?

    I hope to find answers to integrals like [tex]\sqrt{(x-1){x-2}}[/tex]
     
  2. jcsd
  3. Apr 7, 2010 #2
    Did you get un answer for your question?

    I'm dealing with this integral:
    \int_0^{\infty } \frac{(\text{BesselJ}[0,\zeta a]-\text{BesselJ}[0,\zeta b])^2}{\zeta \sqrt{\zeta ^2-k^2}} \, d\zeta
     
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