roots of $J_{\nu} (r x)$ (Bessel function of the first kind)were $r$ is a constant.

Question

Are there any algorithms/formulas that give the zeros of the function $J_{\nu} (r x)$ ?(r is a constant) I have the answer for $J_{\nu} (x)$, but I don't know what to do when $r$ is present.

Thank you for the help.

Answer 1

You scale. The number $x_0$ is a zero of $J_\nu(x)$ if and only if $x_0/r$ is a zero of $J_\nu(rx)$.

I don't know how you obtain the zeros to $J_\nu(x)$, though. Maybe from a table?