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Simplifying to PolyLog

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113494] Simplifying to PolyLog
  • From: Sam Takoy <sam.takoy at yahoo.com>
  • Date: Sun, 31 Oct 2010 02:07:50 -0500 (EST)

Hi,

I'm puzzled by the fact that the first of the following expressions is 
successfully summed while the second, simpler one is not:

In[806]:= Sum[(((-1)^n) (r^n) Cos[a n] )/n^3, {n, 1, Infinity}]
Sum[(((-1)^n) Cos[a n] )/n^3, {n, 1, Infinity}]

Out[806]= 1/2 (PolyLog[3, -E^(-I a) r] + PolyLog[3, -E^(I a) r])

Out[807]= \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)]
\*FractionBox[\(
\*SuperscriptBox[\((\(-1\))\), \(n\)]\ Cos[a\ n]\),
SuperscriptBox[\(n\), \(3\)]]\)

Many thanks in advance,

Sam


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