`whittakerW`

Whittaker function W_{k,m}(z) of the second kind.

Category: Mathematics > Mathematical Functions

Syntax

Y = whittakerW(k, m, z)

Evaluates W_{k,m}(z).

Description

W_{k,m}(z) is the solution of Whittaker's equation that decays for large positive z, behaving like exp(-z/2)*z^k. In terms of Tricomi's function, W_{k,m}(z) = exp(-z/2)*z^(m+1/2)*U(m - k + 1/2, 1 + 2*m, z).

Because it decays, it is the usual choice for bound-state problems such as the radial Coulomb wave equation.

Input arguments

k, m: Parameters of Whittaker's equation.
z: Argument. Scalar or array.

Output arguments

Y: Values of W_{k,m}(z), with the size of z.

Example

Evaluate

whittakerW(1, 2, 3)
whittakerW(0.5, 0, 1)

Output

ans = 2.1177
ans = 0.6065

whittakerW