Spherical Hankel Function of the First Kind
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
"Spherical Bessel Functions." §10.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
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30-3-2019
2319
Spherical Hankel Function of the First Kind
The spherical Hankel function of the first kind 
is defined by
where 
is the Hankel function of the first kind and 
and 
are the spherical Bessel functions of the firstand second kinds.
It is implemented in the Wolfram Language as SphericalHankelH1[n, z].
Explicitly, the first few are
The derivative is given by
![d/(dz)h_n^((1))(z)=1/2[h_(n-1)^((1))(z)-(h_n^((1))(z)+zh_(n+1)^((1))(z))/z].](http://mathworld.wolfram.com/images/equations/SphericalHankelFunctionoftheFirstKind/NumberedEquation1.gif) |
(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.
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. 437-442, 1972.
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 623, 1985.
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