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- Summary:
- For implementing a mode-matching technique in EM simulation, I want to get a closed-form equation of the integral of [tex]\int_{0}^{r}\frac{1}{\rho} J_m(a\rho) J_n(b\rho) d\rho [/tex].

I can only find a solution to [tex] \int_{0}^{r} \rho J_m(a\rho) J_n(b\rho) d\rho [/tex] with the Lommel's integral . The closed form solution to [tex] \int_{0}^{r}\frac{1}{\rho} J_m(a\rho) J_n(b\rho) d\rho [/tex] I am not able to find anywhere. Is there any way in which I can approach this problem from scratch? Here, [tex] J_m [/tex] is the Bessel function of the first kind of order m.

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