MATLAB Function Reference |
Bessel function of the third kind (Hankel function)
Syntax
Definitions
where is a nonnegative constant, is called Bessel's equation, and its solutions are known as Bessel functions. and form a fundamental set of solutions of Bessel's equation for noninteger . is a second solution of Bessel's equation - linearly independent of - defined by
The relationship between the Hankel and Bessel functions is
where is besselj
, and is bessely
.
Description
H = besselh(nu,K,Z)
computes the Hankel function , where K
= 1 or 2, for each element of the complex array Z
. If nu
and Z
are arrays of the same size, the result is also that size. If either input is a scalar, besselh
expands it to the other input's size. If one input is a row vector and the other is a column vector, the result is a two-dimensional table of function values.
H = besselh(nu,K,Z,1)
scales by exp(-i*Z)
if K
= 1, and by exp(+i*Z)
if K
= 2.
[H,ierr] = besselh(...)
also returns completion flags in an array the same size as H
.
Examples
This example generates the contour plots of the modulus and phase of the Hankel function shown on page 359 of [1] Abramowitz and Stegun, Handbook of Mathematical Functions.
It first generates the modulus contour plot
[X,Y] = meshgrid(-4:0.025:2,-1.5:0.025:1.5); H = besselh(0,1,X+i*Y); contour(X,Y,abs(H),0:0.2:3.2), hold on
then adds the contour plot of the phase of the same function.
See Also
besselj
, bessely
, besseli
, besselk
References
[1] Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965.
beep | besseli |
© 1994-2005 The MathWorks, Inc.