Complex Trilogarithm

= Spence's tri-Logarithm.

function t = trilog(z)

trilog = Spence's tri-Logarithm.

t = trilog(z) = Li_3(z)

= Sum From n=1 To n=Infinity Of z^n/n^3 if |z|<=1.

INPUT z: real or complex, scalar, vector or matrix.

OUTPUT t: component-wise trilogarithm of z (accuracy around machine precision).

Depending on the size of the matrix z and of the magnitude of its

components, trilog(z) is 2 to 5 (and more) orders of magnitude

faster than the polylog(3,z) from the Matlab symbolic toolbox.

EXAMPLE: trilog(z) vs polylog(3,z).

N = 10000;

z = 200*( rand(N) + i*rand(N) ) - 100 - i*100;

tic; t=trilog(z); toc;

Elapsed time is 12.081650 seconds.

N = 160;

z = 200*( rand(N) + i*rand(N) ) - 100 - i*100;

tic; t=polylog(3,z); toc;

Elapsed time is 12.289606 seconds.