`whittakerM`

Whittaker function M_{k,m}(z) of the first kind.

Category: Mathematics > Mathematical Functions

Syntax

Y = whittakerM(k, m, z)

Evaluates M_{k,m}(z).

Description

M_{k,m}(z) solves Whittaker's equation w'' + (-1/4 + k/z + (1/4 - m^2)/z^2)*w = 0. It is a rescaled Kummer function: M_{k,m}(z) = exp(-z/2)*z^(m+1/2)*1F1(m - k + 1/2; 1 + 2*m; z).

The second solution is whittakerW. M is the one that is regular at the origin, behaving like z^(m+1/2).

Input arguments

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

Output arguments

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

Example

Evaluate

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

Output

ans = 10.1761
ans = 0.6065

whittakerM