Roots of 𝐽₀(𝑧)-𝑖𝐽₁(𝑧)=0 as saddle points of the reduced logarithmic derivative of 𝐽₀(𝑧)

Abad, Julio; Sesma, Javier

doi:10.1090/qam/1121681

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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