The generalized polylogarithm, also called the Goncharov polylogarithm, is an iterated integral defined recursively by
 |
where 
. For a list of 
zeros, the normalization is
 |
The integral can initially be taken along a positive real segment that avoids the nonzero 
.
Its other branches are obtained by analytic
continuation along paths avoiding 0 and the nonzero 
(Goncharov 2001). For positive
integer 
, the ordinary polylogarithm 
equals 
for 
. Restricting the indices to 
, 
,
and 
also gives the harmonic polylogarithm,
with a factor of 
for each index equal to 1.
The generalized polylogarithm is implemented in the Wolfram Language as GeneralizedPolyLog[{a1, ..., ak}, z].
