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MathGroup Archive 1999

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Re: problems with series of multiple integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18368] Re: problems with series of multiple integrals
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 30 Jun 1999 14:13:30 -0400
  • Organization: Universitaet Leipzig
  • References: <7l5sto$ijk@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,


what is with:

mint[f_[args__], t_] := 
  Integrate @@ {f[args], Sequence @@ ({#, 0, t} & /@ {args})}

Hope that helps

Jens


> Hallo there!
> 
> If have a syntactical problem in the following context: I need to
> evaluate the Durbin algorithm for first passage time of Brownian motion
> for curved boundaries. The density function of the fpt is of the form
> 
> f(t)=sum_{i=1}^\infty q_k(t),
> 
> where each component q_k(t) requires the evaluation of the
> (k-1)-integral of a function of t_0, ..., t_{k-1}, with equal integral
> limits 0 to t.
> 
> I would like to implement the function q_k(t) in the form q[k_, t_], so
> that the body of the routine q would contain
> 
> Integrate[ a function of t_0, ..., t_{k-1}, {t_0, 0, t}, {t_1, 0,t},
> ..., {t_{k-1}, t}]
> 
> That is: The  length of the argument list {t_0, 0, t}, {t_1, 0,t}, ...,
> {t_{k-1}, t} depends on the index k (!!!), which is passed to the
> program q[k,t], so that the argument list must be evaluated dynamically
> by the routine. Is there any way to do this, that is, a syntax that
> Mathematica 3.0 will understand?
> 
> Any hints are appreciated. Thank you very much!


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