PolyLog[2,z]. How does Mathematica do this?
- To: mathgroup at smc.vnet.net
- Subject: [mg2102] PolyLog[2,z]. How does Mathematica do this?
- From: toni at phy.hw.ac.uk (Toni Lee)
- Date: Fri, 29 Sep 1995 01:16:17 -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]
in the range z < -1, 1 < z?
Thanks
---
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| Toni Lee | |
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