`besselh`

Bessel function of the third kind (Hankel function).

Syntax

H = besselh(nu, Z)

Returns the Hankel function of the first kind, order nu.

H = besselh(nu, K, Z)

Selects the kind with K: 1 for H1, 2 for H2.

Description

The Hankel functions combine the Bessel functions of the first and second kind: H1 = J + i*Y and H2 = J - i*Y. They behave like outgoing and incoming waves, which is why they appear in wave propagation and scattering problems.

The two kinds are complex conjugates of each other for real arguments.

Input arguments

nu: Order of the function (real).
K: Kind: 1 or 2. Default is 1.
Z: Real or complex argument.

Output arguments

H: Complex values of the function.

Example

Hankel functions of order 0

besselh(0, 1, 1)
besselh(0, 2, 1)

Output

ans = 0.7652 + 0.0883i
ans = 0.7652 - 0.0883i

besselh