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