Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-29T06:11:01.306Z Has data issue: false hasContentIssue false
  • English
  • Français

A property of the zeros of a cross-product of Bessel functions

Published online by Cambridge University Press:  24 October 2008

D. M. Willis
D. M. Willis
Affiliation:
D.S.I.R. Radio Research Station, Ditton Park, Slough
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 2 , April 1965 , pp. 425 - 428
Copyright
Copyright © Cambridge Philosophical Society 1965

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Fletcher, A., Miller, J. C. P., Rosenhead, L. and Comrie, L. J.An index of mathematical tables, vol. 1 (Scientific Computing Service; London, 1962).Google Scholar
(2)Gray, A., Mathews, G. B. and Macrobert, T. M.A treatise on Bessel functions and their applications to physics (Macmillan; London, 1922).Google Scholar
(3)McMahon, J.Ann. of Math. 9 (1895), 23–30.CrossRefGoogle Scholar
(4)Watson, G. N.A treatise on the theory of Bessel functions (2nd ed.; Cambridge, 1944).Google Scholar