`kummerU`

Confluent hypergeometric function of the second kind U(a, b, z).

Category: Mathematics > Mathematical Functions

Syntax

Y = kummerU(a, b, z)

Evaluates Tricomi's confluent hypergeometric function U(a,b,z).

Description

U(a,b,z) is the second linearly independent solution of Kummer's differential equation z*w'' + (b - z)*w' - a*w = 0, chosen so that it decays like z^(-a) for large positive z. The first solution is the Kummer function 1F1(a;b;z).

For a = 1 and b = 2 the function reduces to 1/z, which gives a quick check on the numbers.

Input arguments

a, b: Parameters of the function.
z: Argument. Scalar or array.

Output arguments

Y: Values of U(a,b,z), with the size of z.

Example

Check against 1/z

kummerU(1, 2, [1 2 3])
kummerU(0.5, 1, 2)

Output

ans = 1×3

    1.0000    0.5000    0.3333
ans = 0.6457

kummerU