Table of First 700 Zeros of Bessel Functions - J l (x) and J' l (x)

The zeros of the Bessel functions and Bessel function deriviatives are identified, by standard waveguide notation which also sej-ves as a code for more general mathematical applications. The possibilities of low-loss transmission using the TEoi (circular electric) mode in circular cylindrical pipe of a diameter large compared to the wavelength has made the study of other modes of such a waveguide important. In order to find phase and attenuation constants of various modes for both solid and ring or helix walls, the zeros of the Bessel functions Ji{x) and J'i(x) are essential. In the table given here the first seven hundred roots of Bessel functions Ji(x) = 0 and J'i(x) = 0 have been computed and arranged in the order of the magnitude of the arguments corresponding to the roots. In the table I is the order of the Bessel function and m is the serial number of the zero of either Ji(x) or J'i(x), not counting x = 0. In waveguide applications the zeros of Ji{x) correspond to transverse magnetic modes of propagation (TM modes) and those of J'i(x) to transverse electric modes (TE modes). The designations TM and TE appear in the table for the benefit of those who will use this table in waveguide research and serve as a code designating Ji(x) and J'i(x) for those who are interested in a more general application of the mathematics. The roots of the Bessel functions were calculated from the Tables of the Bessel Functions of the First Kind of Orders, J through «/ , computed by the Staff of the Computation Laboratory of Harvard University, published by the Harvard University Press, 1946-1948.