integral multiple infinite limits

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kostas
kostas 2011-9-2
Hi , i have to solve one more difficult integral...its an integral like this
fun=∫[exp(-u^2)*(∫fun1(v,u,x,Kt)dv)*(∫fun2(v,u,x,Kt)dv]du
The limits are for v[1e-9,Inf] and u[-inf,inf]
I tried to transform the function mydblquad of Mike Hossea http://www.mathworks.com/matlabcentral/answers/14514-double-integral-infinite-limits but i didn't manage to do it..Is there any idea??? Thanks!!!

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Mike Hosea
Mike Hosea 2011-9-2
Try this:
function q = paris(fun1,fun2,x,Kt)
% q = ∫[exp(-u^2)*(∫fun1(v,u,x,Kt)dv)*(∫fun2(v,u,x,Kt)dv]du
% The limits are 1e-9 <= v < inf and -inf < u < inf.
a = 1e-9;
innerintegral = @(u) ...
arrayfun(@(u1) ... % u1 is always a scalar here.
exp(-u1^2) * ...
quadgk(@(v)fun1(v,u1*ones(size(v)),x,Kt),a,inf) * ...
quadgk(@(v)fun2(v,u1*ones(size(v)),x,Kt),a,inf), ...
u);
q = quadgk(innerintegral,-inf,inf);
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Mike Hosea
Mike Hosea 2011-9-2
If fun1 and fun2 are m-files, you need to use "@", i.e. paris(@fun1,@fun2,x,Kt). You leave off the "@" when they are instead variables to which you have stored anonymous functions. Note that the way I set it up, fun1 and fun2 are both functions of 4 variables: v, u, x, and Kt.
kostas
kostas 2011-9-2
Ok , that works perfect!!
Thanks a lot again!!!

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