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Math Help - Integration over a finite interval containing simple poles, any application?

  1. #1
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    Integration over a finite interval containing simple poles, any application?

    My problem in short is an application of the following theorem, as found in:


    Dragoslav S. Mitrinović and Jovan D. Kecić , The Cauchy Method of Residues , 1984 , D. Reidel Publishing Company, theorem 1, chapter 5.4.2, pages 184-185.


    Suppose that the following conditions are satisfied:
    1 The function f is holomorphic in the extended plane, except for in a finite amount of singularities.
    2. On the interval (a,b) of the real axis f may have only simple poles.
    Suppose that the following conditions are satisfied:
    3. f has no singularities at {a, b}.


    For the theorem in a latex enviroment, see the stack exchange link.


    Are there any applications you know of? All I know of are fun demonstrations of how it works, but nothing 'real'.
    What I primarily have in mind is within the areas of statistics or physics (theoretical or not).


    This is a cross post across:
    [Mathoverflow]
    [PhysicsForums]
    [Thephysicsforum]
    [Statisticsforum]
    [Mathhelpforum]

    Edit: Regarding the links, I'll make sure they're up and running as soon as those at physicsforums realize that this isn't math solely.
    Last edited by Elendur; March 19th 2014 at 05:35 AM.
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  2. #2
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    Re: Integration over a finite interval containing simple poles, any application?

    I am not positive, but I think this occurs in Bayesian networks where you find Dirichlet multinomial distributions that are part of some larger network. You can collapse each Dirichlet prior when certain conditions hold. I think the conditions (in some instances) can be expressed mathematically as something similar to what you posted. But, I have only glanced at this material, so I may be way off.
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  3. #3
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    Re: Integration over a finite interval containing simple poles, any application?

    Any possible leads are welcomed with open arms thanks a lot! I'll look into it at first best opportunity.
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