Re: Help with Multiple Integrals
- To: mathgroup at smc.vnet.net
- Subject: [mg19543] Re: [mg19468] Help with Multiple Integrals
- From: "Wolf, Hartmut" <hwolf at debis.com>
- Date: Tue, 31 Aug 1999 00:52:29 -0400
- Organization: debis Systemhaus
- References: <199908281953.PAA24442@smc.vnet.net.>
- Sender: owner-wri-mathgroup at wolfram.com
Andrew Wang schrieb: > > I'm new to Mathematica and I need to solve a summation in which each > term has a different number of multiple integrals. To be more specific, > my n-th term should look like: > > g[n] NIntegrate[ f[n], {x1, a,b},{x2, x1, b}, ... , {xn, xn-1,b}]; > > a,b are constants and f[n] is an expression that involves x1, x2, ..., > xn (so each term has a different number of integration variables), with > n going from 1 to N. I could define all the N terms of my summation but > since N is really large, it's unfeasible to do it manually. Is there any > way of defining a function in Mathematica to build and evaluate each > term given n? I could also write a script not in Mathematica to build > all the terms and save them on a file to be read from Mathematica, but > is it possible to do it in Mathematica (to use string manipulation to > "build" the n-th term and then evaluate it)? > If you define recursively In[1]:= ivr[1] = {x1, a, b}; In[2]:= ivr[n_] := Sequence[ivr[n - 1], {ToExpression["x" <> ToString[n]], ToExpression["x" <> ToString[n - 1]], b}] you get In[3]:= g[#] NIntegrate[f[#], Evaluate[ivr[#]]] & @4 NIntegrate::"nlim": "\!\(x1\) = \!\(a\) is not a valid limit of integration." Out[3]= g[4] NIntegrate[f[4], {x1, a, b}, {x2, x1, b}, {x3, x2, b}, {x4, x3, b}] So when you Map it over Range[N] you'll get a List of all your integrals. (Of course you shall not get the error since you defined everthing.) Kind regards, hw
- References:
- Help with Multiple Integrals
- From: Andrew Wang <ke@bu.edu>
- Help with Multiple Integrals