$$\int_{0}^R \rho J_0\left(\frac \rho {\sqrt \tau} \right) J_0 \left(k_n \rho \right) d\rho = -\frac {{R^3}/{\sqrt \tau}}{x_n^2-{R^2}/{\sqrt \tau}} J_1\left(\frac{R}{\sqrt \tau}\right) J_0(x_n)$$
I want to show the above. Can anyone help?
2026-04-01 21:51:44.1775080304
difficult integral with bessel functions
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