Definite integration of bessel function as a function of ρ, φ

Question

I want to know how I can analytically integrate below function.

$\int_0^{2\pi}\int_b^a J_0(\lambda\sqrt{\rho^2+r^2-2r\rho\cos\phi})\rho d\rho d\phi$

Please let me know (r is constant value). If there is no way to integrate this function, should I use numerical integration?