Hankel functions
From Encyclopedia of Mathematics
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Cylinder functions of the third kind. They may be defined in terms of Bessel functions as follows:
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where 
is not an integer. This implies the important relations
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Hankel functions are complex for real values of 
; however,
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are real if 
is real and positive. Hankel functions have simple asymptotic representations for large 
:
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The Hankel function of a "half-integral" argument 
can be expressed in terms of elementary functions, in particular:
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These functions were introduced by H. Hankel in 1869.
References
| [1] | E. Jahnke, F. Emde, F. Lösch, "Tafeln höheren Funktionen" , Teubner (1966) |
Comments
See Cylinder functions for additional references.
How to Cite This Entry:
Hankel functions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hankel_functions&oldid=17400
Hankel functions. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hankel_functions&oldid=17400
This article was adapted from an original article by P.I. Lizorkin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article