I would like to calculate the next integral for different values to the parameter $w$
$\int_{0}^{\infty}{du}\int_{0}^{\infty}{dv} \frac{u}{u^2+v^2}\left(\int_{0}^{0.8}\int_{0}^{\infty} xe^{-2w\sqrt{x^2+y^2}} J_{0}(ux)[cos(\pi y/0.8)]^2 cos(yv) {dy}{dx}\right)^2$
I am trying first to define the double integral Inside of the square:
f[u_, v_, w_?NumericQ] :=NIntegrate[x*Exp[-2*w*Sqrt[x^2 + y^2]]*BesselJ[0, u*x]*Cos[y*v]*(Cos[Pi*y/0.30040290])^2, {x, 0, Infinity}, {y, 0, 0.30040290/2},Method -> "QuasiMonteCarlo"]
and after to integrate this expression with respect to $u$ and $v$ for a given value of $w$, for example 4
NIntegrate[ (u/(u^2 + v^2))*((f[u_, v_,4])^2), {u, 0, Infinity}, {v, 0, Infinity}, Method -> "QuasiMonteCarlo"]
Of course something is wrong in my reasoning because I get this warning message:
NIntegrate::inumr: The integrand E^(-4 Sqrt[x^2+y^2]) x BesselJ[0,x u_] Cos[10.4579 y]^2 Cos[y v_] has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,1},{0,1}}.
Thank you for all your help
Clear[f]
. You probably have an old def forf
without theNumericQ
$\endgroup$f
to have the signaturef[u_?NumericQ, v_?NumericQ, w_?NumericQ]
. $\endgroup$