Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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: 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.


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


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