Roots of \(J_ \gamma(z)\pm iJ_{\gamma+1} (z)=0\) and the evaluation of integrals with cylindrical function kernels. (English) Zbl 0798.33003
With the usual notation for Bessel functions of integer order, the authors show that \(J_ n\pm J_{n+1}\) has no zeros in the lower (upper) half plane. The zeros of this function are tabulated for \(n=1,2\). The note includes Cartesian maps (mappings of constant coordinate lines) of \(J_ 0+ iJ_ 1\), and \(J_ 1- iJ_ 2\).
Reviewer: D.Kershaw (Lancaster)
MSC:
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
