I have following integration. $$I=\int_{0}^{\frac{\pi}{2}} \int_{0}^{\infty} \gamma e^{- \lambda \left(\gamma^2+2d\gamma\cos\theta -d^2 + \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} 2d\cos\Theta(d\cos\Theta - \sqrt{d^2\cos^2\Theta + 2d\gamma\cos\theta+\gamma^2}) d\Theta \right) } \,d\gamma d\theta$$ Since this may not have a closed-form solution, I tried to evaluate it numerically as below:
PoNum[λ_, d_] :=NIntegrate[
NIntegrate[
x Exp[-λ (x^2 + 2 d x Cos[θ] - d^2 +
NIntegrate[
2 d Cos[Θ] (d Cos[Θ] -
Sqrt[(d Cos[Θ])^2 + 2 d x Cos[θ] +
x^2]), {Θ, -(π/2), π/2}])], {x,
0, ∞}], {θ, 0, π/2}];
Here $\lambda$ and $d$ are positive constant. E.g.
PoNum[2.3, 1.1]
However, my code may not give correct answer as I have seen series of warnings.
Can someone please help me?