|MATLAB Function Reference|
Bessel function of the third kind (Hankel function)
The differential equation
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
besselj, and is
H = besselh(nu,K,Z)
computes the Hankel function , where
K = 1 or 2, for each element of the complex array
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,Z)
K = 1.
H = besselh(nu,K,Z,1)
K = 1, and by
K = 2.
[H,ierr] = besselh(...)
also returns completion flags in an array the same size as
||Some loss of accuracy in argument reduction.
||Unacceptable loss of accuracy,
||No convergence. Returns
This example generates the contour plots of the modulus and phase of the Hankel function shown on page 359 of  Abramowitz and Stegun, Handbook of Mathematical Functions.
It first generates the modulus contour plot
then adds the contour plot of the phase of the same function.
 Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965.