Integration of Bessel's functions

• A
Summary:
For implementing a mode-matching technique in EM simulation, I want to get a closed-form equation of the integral of $$\int_{0}^{r}\frac{1}{\rho} J_m(a\rho) J_n(b\rho) d\rho$$.
I can only find a solution to $$\int_{0}^{r} \rho J_m(a\rho) J_n(b\rho) d\rho$$ with the Lommel's integral . The closed form solution to $$\int_{0}^{r}\frac{1}{\rho} J_m(a\rho) J_n(b\rho) d\rho$$ I am not able to find anywhere. Is there any way in which I can approach this problem from scratch? Here, $$J_m$$ is the Bessel function of the first kind of order m.

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