Zeros of Bessel functions

Summary

The zeros of a Bessel function of the first kind $J_\nu$ with $\nu > -1$ are real. Its positive zeros form an increasing sequence $j_{\nu,1} < j_{\nu,2} < \cdots$ tending to infinity. These numbers fix the frequencies of a vibrating circular drum and the modes of heat flow in a cylinder. They obey interlacing and spacing rules, and they are the subject of Bourget's hypothesis.