Integration with branch cuts

  • Thread starter krindik
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  • #1
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Main Question or Discussion Point

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]
 

Answers and Replies

  • #2
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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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