In this note a new proof for the classical theorem of Hurwitz on the exact number of complex zeros of Bessel functions of the first kind is given. The proof is based on the closed form of the determinant of a symmetric Hankel matrix whose terms are Rayleigh sums of the zeros of Bessel functions and on some new interesting results on entire functions of finite growth order of Kytmanov and Khodos [khodos].
Starlikeness of Bessel functions and their derivatives
On the $n$-th derivative and the fractional integration of Bessel functions with respect to the order
Uniform asymptotic expansions for the zeros of Bessel functions
![QR code for arXiv:1708.07729 [math.CA]](http://oss.arxitics.com/images/favicon.svg)