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MathGroup Archive 1999

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Re: problems with series of multiple integrals

  • To: mathgroup at
  • Subject: [mg18348] Re: [mg18335] problems with series of multiple integrals
  • From: "Carl K.Woll" <carlw at>
  • Date: Wed, 30 Jun 1999 14:13:19 -0400
  • Organization: Department of Physics
  • References: <>
  • Sender: owner-wri-mathgroup at

Hi Thomas,

I think the key here is to prevent Integrate from evaluating until you have
set up the integral properly. Here are two ideas:




In the function q1[k,s] I use Block to prevent Integrate from evaluating,
then I set up the integral. Once Block is exited, Integrate does its thing.
For the integrand I just used a sum of the integration variables, and
instead of subscripts t_i I used t[i]. You can certainly use subscripted
variables if you want, I didn't use them because they don't look pretty in
email. The second function does essentially the same thing. I form the
integral with a dummy head, and then I replace dummy with Integrate. The
functions work:

3 s

Good luck.

Carl Woll
Physics Dept
U of Washington

Dr. Thomas Burkhardt wrote:

> 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!
> --
> -------------------------------------------------------------
> Dr. Thomas Burkhardt
> e-mail: tburkha at
> Tel.:   +49-3731-39-2420
> FAX:    +49-3731-39-4053
> Fakultaet Wirtschaftswissenschaften
> Technische Universitaet BA Freiberg
> Gustav-Zeuner-Str. 10
> D-09596 Freiberg
> Germany

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