Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Roots of $ J_0(z)-iJ_1(z)=0$ as saddle points of the reduced logarithmic derivative of $ J_0(z)$


Authors: Julio Abad and Javier Sesma
Journal: Quart. Appl. Math. 49 (1991), 495-496
MSC: Primary 33C10
DOI: https://doi.org/10.1090/qam/1121681
MathSciNet review: MR1121681
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Abstract | References | Similar Articles | Additional Information

Abstract: The roots of $ {J_0}\left( z \right) - i{J_1}\left( z \right) = 0$ are saddle points of the function $ {F_0}\left( z \right) \equiv \\ z{J'_0}\left( z \right)/{J_0}\left( z \right)$. A very efficient algorithm allows one to obtain, by iteration, those roots to the desired accuracy.


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] A. D. Rawlins, Note on the roots of $ f\left( z \right) = {J_0}\left( z \right) - i{J_1}\left( z \right)$, Quart. Appl. Math. 47, 323-324 (1989) MR 998105
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  • [4] M. Abramowitz and I. A. Stegun (Editors), Handbook of Mathematical Functions, Dover, New York, 1965
  • [5] A. Cruz and J. Sesma, Modulus and phase of the reduced logarithmic derivative of the cylindrical Bessel function, Math. Comp. 35, 1317-1324 (1980) MR 583509

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DOI: https://doi.org/10.1090/qam/1121681
Article copyright: © Copyright 1991 American Mathematical Society

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