Polylogarithm Evaluation

Defining a polylogarithm by:

g(x,z) = \sum_{n=1}^\infty z^n/n^x

where all quantities are real, can anyone point me
to a reasonable method for the computation of g when
z is less than but very close to 1? In the problems
I am interested in z = 3/2 or 1/2 and 0 \le x \le 1

This is, of course, \zeta(x) when z = 1.

These functions occur in the discussion of the condensation
of an ideal Bose-Einstein gas.

Thanks in advance.

--
--- Paul J. Gans
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