# Question:multiple integration

## Question:multiple integration

Maple
I am trying to calculate numerically a triple integral of a function (see below). However I could not get a result. I stopped the calculation after one hour of evaluation. One of the integral is from 0 to infinity and uses NAG d01amc. The 2 other integrals have finite bounds and use NAG _d01ajc. I also tried to use maple default integration algorithms for the 2 finite bounds integrals but without success. in the following xs, ys, zs, k, k_0, x, y, rho_0 and d are real numbers. k_m, rho_me, nu_m are complex numbers. The variable sof integration are k (from 0 to +infinity), x (from -1 to +1) and y (from -1.5 to 1.5). Here is the Maple script. restart; Digits := 15; nu_0 := sqrt(k^2 - k_0^2); nu_m := sqrt(k^2 - k_m^2); pref2 := 2*rho_me*exp(-nu_0*(zs + z))*BesselJ(0, k*sqrt((xs - x)^2 + (ys - y)^2))*k/(rho_me*nu_0 + rho_0*nu_m*tanh(nu_m*d)); (evalf@Int)(eval(0.5*Re(`~`[evalf@Int]((Re + Im*I)(eval(pref2, [z = 0, k_0 = 0.018371886863098, xs = 0, ys = 0, zs = 10, rho_0 = 1.2, d = 0.04, rho_me = 1.528516816439260 - 1235.297048886680*I, k_m = 0.490806242885258 - 0.490314205803914*I])), k = 0 .. infinity, epsilon = 0.1*10^(-5), method = _d01amc)), [z = 0, k_0 = 0.018371886863098, xs = 0, ys = 0, zs = 10, rho_0 = 1.2, d = 0.04, rho_me = 1.528516816439260 - 1235.297048886680*I, k_m = 0.490806242885258 - 0.490314205803914*I]), [x = -2/2 .. 2/2, y = -3/2 .. 3/2], epsilon = 0.1*10^(-5), method = _d01ajc); Thanks for the help.
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