Complex Dilogarithm

Dilogarithm of any complex numbers

Description

dilog(z) returns the (component-wise) dilogarithm of z. It is quite fast and accurate (around machine precision).

The present dilog function corresponds to Maple's polylog(2,z) and Mathematica's PolyLog[2,z] functions.

It is defined as
dilog(z) = sum_{n=1}^Inf z^n/n^2
for |z|<=1, and by analytic continuation for |z|>1.

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[Richard Alexander]

Results appear to be wrong!
For example:
dilog(100) = -12.19242 according to Maple
dilog(100) = -7.324 -14.467i according to this.

[Didier Clamond]

They are several definitions of the dilogarithm. The present M-file corresponds
to Maple's polylog(2,z) function and NOT its
dilog function. Maple 8 says:
evalf(polylog(2,100)) = -7.323953199-14.46756882*I
which is what the M-file gives.

The definition is clearly explained in the header of dilog.m. You should read it.

[lian tuma]

 

[Marcelo Pisani]

 

[Marcelo Pisani]

except for x=0.5, this function gives incorrect results for x in the interval [0 2]

[Didier Clamond]

I don't see what's wrong with dilog.m for x in the interval [0 2].
For example,

with Matlab R2007a:
dilog(0.25)
ans = 0.267652639082733

with Mathematica 5.2:
N[PolyLog[2, 1/4], 17]
ans = 0.26765263908273261

[Marcelo Pisani]

x = linspace(-10,10,256)';
d1 = dilog(x);
d2 = zeros(size(x));
for ii = 1:numel(d2)
    d2(ii) = str2double(maple(sprintf('evalf(polylog(2,%g))',x(ii))));
end
clf;
subplot(2,1,1); plot(x,[real(d1) real(d2)]); ylabel('real');
subplot(2,1,2); plot(x,[imag(d1) imag(d2)]); ylabel('imag');
legend({'dilog(x)' 'polylog(2,x)'});
xlabel('x');

[Didier Clamond]

I still don't find the problem.
I don't have access to Matlab's symbolic toolbox.
My guess is that you loose accuracy somewhere in converting string to numeric, or something like that. Please, read your manual.

[Marcelo Pisani]

The code works as expected, unfortunately File exchange does not allow to edit past ratings and I could not revise it. Even worse, the low rate was entered twice when I was trying to correct it.