A property of the zeros of a cross-product of Bessel functions
- 1 April 1965
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 61 (2) , 425-428
- https://doi.org/10.1017/s0305004100003984
Abstract
In this note it is shown that any positive root of the transcendental equation is definable as a continuous increasing function of the real variable ν, provided ν is positive. Here Jν and Yν denote respectively the Bessel functions of the first and second kind of order ν, and k is a positive constant. Watson ((4)) has established the corresponding result for the simpler equations Jν(z) = 0 and Jν(z) cosα − Yν(z) sinα = 0, where α is a constant. The extension of the result to the positive roots of equation (1) is important because this equation occurs quite frequently in physical problems.This publication has 1 reference indexed in Scilit:
- On the Roots of the Bessel and Certain Related FunctionsAnnals of Mathematics, 1894