Modulus and phase of the reduced logarithmic derivative of the Hankel function

The modulus and phase of the reduced logarithmic derivative of the Hankel function $$zH^{(1)'}_\nu(z)/H^{(1)}_\nu(z)$$ for complex variable $z$ and real order $\nu$, are investigated. Special attention is paid to the location of saddle points and their trajectories as $\nu$ varies.

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Bibliographic Details
Published in:Mathematics of computation 1983-01, Vol.41 (164), p.597-605
Main Authors: Cruz, Andrés, Sesma, Javier
Format: Article
Language:English
Subjects:
Bessel functions
Hankel functions
Infinity
Integers
Mathematical functions
Quadrants
Saddle points
Symmetry
Trajectories
Zero
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Summary:The modulus and phase of the reduced logarithmic derivative of the Hankel function $$zH^{(1)'}_\nu(z)/H^{(1)}_\nu(z)$$ for complex variable $z$ and real order $\nu$, are investigated. Special attention is paid to the location of saddle points and their trajectories as $\nu$ varies.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1983-0717705-3