besselh (MATLAB Function Reference)

Bessel functions of the third kind (Hankel functions)

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

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:

Description

H = besselh(nu,K,Z)

for K = 1 or 2 computes the Hankel functions

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.

H = besselh(nu,1,Z,1)

scales

by exp(-i*z).

H = besselh(nu,2,Z,1)

scales

by exp(+i*z).

[H,ierr] = besselh(...)

also returns an array of error flags:


`ierr = 1`	Illegal arguments.
`ierr = 2`	Overflow. Return `Inf`.
`ierr = 3`	Some loss of accuracy in argument reduction.
`ierr = 4`	Unacceptable loss of accuracy, `Z` or `nu` too large.
`ierr = 5`	No convergence. Return `NaN`.

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