The spherical Hankel function of the second kind is defined by
where is the Hankel
function of the second kind and and are the spherical
Bessel functions of the first and second
kinds.
It is implemented in Wolfram Language Version 6 as SphericalHankelH2[n,
z].
Explicitly, the first few are given by
The derivative is given by

(7)

The plot above shows the real and imaginary parts of on the real axis for , 1, ..., 5.
The plots above shows the real and imaginary parts of in the complex plane.
See also
Hankel Function of the Second Kind,
Spherical
Hankel Function of the First Kind
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References
Abramowitz, M. and Stegun, I. A. (Eds.). "Spherical Bessel Functions." §10.1 in Handbook
of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 437442, 1972.Arfken, G. Mathematical
Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 623,
1985.Referenced on WolframAlpha
Spherical Hankel
Function of the Second Kind
Cite this as:
Weisstein, Eric W. "Spherical Hankel Function of the Second Kind." From MathWorldA Wolfram Web Resource.
https://mathworld.wolfram.com/SphericalHankelFunctionoftheSecondKind.html
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