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MathGroup Archive 1999

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problems with series of multiple integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg18335] problems with series of multiple integrals
  • From: "Dr. Thomas Burkhardt" <tburkha at bwl.tu-freiberg.de>
  • Date: Sun, 27 Jun 1999 15:11:23 -0400
  • Organization: Technische Universitaet Bergakademie Freiberg
  • Sender: owner-wri-mathgroup at wolfram.com

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 bwl.tu-freiberg.de
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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