An Extended Table of Zeros of Cross Products of Bessel Functions

摘要

The report contains tables of the first five roots of the following transcendental equations: (a) J0(alpha) Y0(alpha) = Y0(alpha) J0(alpha); (b) J1(alpha) Y1(alpha) = Y1(alpha) J1(alpha); (c) J0(alpha) Y1(alpha) = Y0(alpha) J1(alpha) where J0(alpha), Y0(alpha), J1(alpha), Y1(alpha) are Bessel functions of order 0 and 1 respectively. In these equations, alpha is the unknown and k is a parameter which may assume any positive value, other than 0 or 1. Additional tables are included listing an auxiliary quantity gamma which is better suited to interpolation particularly when k is close to unity. (Author)