Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The roots of $ J_0(z)-iJ_1(z)=0$

Author: D. A. Macdonald
Journal: Quart. Appl. Math. 47 (1989), 375-378
MSC: Primary 33A40
DOI: https://doi.org/10.1090/qam/998110
MathSciNet review: 998110
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Abstract | References | Similar Articles | Additional Information

Abstract: Synolakis [1] has proved that the equation

$\displaystyle {J_0}\left( z \right) - i{J_1}\left( z \right) = 0$

has no zeros in the half plane Im $ z > 0$. In this note a table of the first thirty roots, correct to $ O\left( {{{10}^{ - 6}}} \right)$, is presented and an asymptotic formula, which is correct to better than one tenth of one percent for the smallest zero, is derived.

References [Enhancements On Off] (What's this?)

  • [1] C. E. Synolakis, On the roots of $ f\left( z \right) = {J_0}\left( z \right) - i{J_1}\left( z \right)$, Quart. Appl. Math. 46, 105-107 (1988) MR 934685
  • [2] G. F. Carrier, Gravity waves of water of variable depth, J. Fluid Mech. 24, 641-659 (1966) MR 0200009
  • [3] C. E. Synolakis, The runup of solitary waves, J. Fluid Mech. 185, 523-545 (1987)
  • [4] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, 1927 MR 1424469

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DOI: https://doi.org/10.1090/qam/998110
Article copyright: © Copyright 1989 American Mathematical Society

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