Spherical Hankel Function of the Second 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:
...
30-3-2019
2417
Spherical Hankel Function of the Second Kind
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
![d/(dz)h_n^((2))(z)=1/2[h_(n-1)^((2))(z)-(h_n^((2))(z)+zh_(n+1)^((2))(z))/z].](http://mathworld.wolfram.com/images/equations/SphericalHankelFunctionoftheSecondKind/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.
الاكثر قراءة في التفاضل و التكامل
اخر الاخبار
اخبار العتبة العباسية المقدسة
