`polylog`

Polylogarithm Li_n(z).

Category: Mathematics > Mathematical Functions

Syntax

Y = polylog(n, z)

Evaluates the polylogarithm of order n at z.

Description

The polylogarithm is defined for abs(z) < 1 by the series z + z^2/2^n + z^3/3^n + ... and continued analytically elsewhere. Special orders have closed forms: Li_1(z) = -log(1 - z), Li_0(z) = z/(1 - z), and Li_2 is the dilogarithm, with Li_2(1) = pi^2/6.

For real z beyond 1 the principal branch is complex.

Input arguments

n: Order of the polylogarithm.
z: Argument, real or complex, scalar or array.

Output arguments

Y: Values of Li_n(z), with the size of z.

Example

Orders 1 and 2

polylog(1, 0.5)
-log(1 - 0.5)
polylog(2, [0 0.5 -1])
polylog(2, 1)
pi^2/6

Output

ans = 0.6931
ans = 0.6931
ans = 1×3

         0    0.5822   -0.8225
ans = 1.6449
ans = 1.6449

polylog