Simple proofs of classical results on zeros of $\mathbf{J_\nu(x)}$ and $\mathbf{J_\nu'(x)}$

Abstract

The Bessel functions $J_{\nu}(x)$ and their derivatives $J_{\nu}^{\prime}(x)$ can be represented by infinite series and infinite products. Using these representations we give very simple proofs for known results concerning the zeros of the above functions.