MATLAB Function Reference Volume 1: A - E - Bad Request

esselh
2besselh
Purpose Bessel functions of the third kind (Hankel functions)
Syntax H = besselh(nu,K,Z)
H = besselh(nu,Z)
H = besselh(nu,1,Z,1)
H = besselh(nu,2,Z,1)
[H,ierr] = besselh(...)
Definitions The differential equation
2-136
z 2
z 2
2
d y
d
z dy
------ z
dz
2 ν 2
+ + ( – )y=
0
where ν is a nonnegative constant, is called Bessel’s equation, and its solutions
are known as Bessel functions. Jν( z)
and J– ν(
z)
form a fundamental set of
solutions of Bessel’s equation for noninteger ν . Y ν( z)
is a second solution of
Bessel’s equation—linearly independent of Jν( z)
— defined by
Y ν( z)
Jν( z)
cos( νπ)
– J– ν(
z)
= ----------------------------------------------------------sin(
νπ)
The relationship between the Hankel and Bessel functions is
( 1)
Hν ( z)
= Jν( z)
+ i Yν( z)
H2ν ( z)
= Jν( z)
– i Yν( z)
Description H = besselh(nu,K,Z) for K = 1 or 2 computes the Hankel functions
( 1)
( 2)
Hν ( z)
or Hν ( z)
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, it
is expanded 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) uses K = 1.
( 1)
H = besselh(nu,1,Z,1) scales Hν ( z)
by exp(-i*z).
( 2)
H = besselh(nu,2,Z,1) scales Hν ( z)
by exp(+i*z).