PolyLog[2,z]. How does Mathematica do it?

*To*: mathgroup at smc.vnet.net*Subject*: [mg2101] PolyLog[2,z]. How does Mathematica do it?*From*: toni at phy.hw.ac.uk (Toni Lee)*Date*: Fri, 29 Sep 1995 01:16:06 -0400*Organization*: Physics Department, Heriot-Watt University

I am looking for a series expansion for PolyLog[2,z] for z < -1, 1 < z. The Mathematica book gives the series expansion PolyLog[2,z] = Sum[z^k/k^2,{k,1,Infinity}] but this is only true for -1 < z < 1. But Mathematica is still able to evaluate the PolyLog outside this range: Out[2]= -PolyLog[2, -z] In[4]:= %2 /. z -> 0.34816719688504 Out[4]= 0.321798 <-- I can get this with the series expansion In[5]:= %2 /. z -> 45.882645712556 Out[5]= 8.94273 <-- How does Mathematica do this? How does Mathematica evaluate PolyLog[2,z] for z < -1, 1 < z? Thanks --- __________________________________________________________________ | | | | Toni Lee | | | Physics Department, | Tel: +44 (0)131-451-3046 | | Heriot-Watt University, | Fax: +44 (0)131-451-3136 | | Edinburgh, EH14 4AS, | | | Scotland. | Internet: toni at phy.hw.ac.uk | |____________________________|_____________________________________|