Asymptotic relation for zeros of cross-product of Bessel functions and applications

Vladimir Bobkov

Let $a_{\nu ,k}$ be the $k$-th positive zero of the cross-product of Bessel functions $J_{\nu }(Rz)Y_{\nu }(z)-J_{\nu }(z)Y_{\nu }(Rz)$, where $\nu \ge 0$ and $R>1$. We derive an initial value proble…