Skip to main content

A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations

  • F. W. J. Olver (a1)

The zeros of solutions of the general second-order homogeneous linear differential equation are shown to satisfy a certain non-linear differential equation. The method here proposed for their determination is the numerical integration of this differential equation. It has the advantage of being independent of tabulated values of the actual functions whose zeros are being sought. As an example of the application of the method the Bessel functions Jn(x), Yn(x) are considered. Numerical techniques for integrating the differential equation for the zeros of these Bessel functions are described in detail.

Hide All
(1)Bickley, W. G., Miller, J. C. P. and Jones, C. W.Notes on the evaluation of zeros and turning values of Bessel functions. Phil. Mag. 36 (1945), 121–33 and 200–10.
(2)Milne-Thomson, L. M.Calculus of finite differences (Macmillan, 1933).
(3)Fox, L. and Goodwin, E. T.Some new methods for the numerical integration of ordinary differential equations. Proc. Cambridge Phil. Soc. 45 (1949), 373–88.
(4)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).
(5)Bickley, W. G.Formulae relating to Bessel functions of moderate or large argument and order. Phil. Mag. 34 (1943), 371–49.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 10 *
Loading metrics...

Abstract views

Total abstract views: 79 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th July 2018. This data will be updated every 24 hours.