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Re: Help with Multiple Integrals
*To*: mathgroup at smc.vnet.net
*Subject*: [mg19521] Re: [mg19468] Help with Multiple Integrals
*From*: BobHanlon at aol.com
*Date*: Sun, 29 Aug 1999 03:00:40 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Clear[a, b, f, g, n];
k = 3;
var = Table[ToExpression["x" <> ToString[i]], {i, k}];
lim = ReplacePart[RotateRight[var], a, 1];
iter = Transpose[{var, lim, Table[b, {k}]}];
This is the form required
g[n]*Integrate[f[var, n], Evaluate[Sequence @@ iter]]
g[n]*Integrate[f[{x1, x2, x3}, n], {x1, a, b}, {x2, x1, b},
{x3, x2, b}]
For a specific function
g[n]*Integrate[x1^n * x2^(n - 1)*x3, Evaluate[Sequence @@ iter]];
% /. {n -> 3, a -> 1., b -> 5.}
7698.996825396825*g[3]
Using NIntegrate
n = 3; a = 1; b = 5;
g[n]*NIntegrate[x1^n * x2^(n - 1)*x3, Evaluate[Sequence @@ iter]]
7698.996836118737*g[3]
Bob Hanlon
In a message dated 8/28/99 7:51:21 PM, ke at bu.edu writes:
>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)?
>
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