I have a mechanical engineering background. Can someone help me to find out zeroes of Bessel function?
$$\Gamma(f,\beta)=\sum_{k=1}^\infty J_1(f\alpha_k)\tanh(a_k\beta)/[\alpha_k^2J_0^2(\alpha_k)]$$
I know the value of $f$ and $\beta$. How can I find $\alpha$? They are the zeros of Bessel function $J_1(x)$.