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MathGroup Archive 1995

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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         |
|____________________________|_____________________________________|





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