Re: Simplifying to PolyLog

*To*: mathgroup at smc.vnet.net*Subject*: [mg113525] Re: Simplifying to PolyLog*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Mon, 1 Nov 2010 05:00:34 -0500 (EST)

On 10/31/10 at 2:07 AM, sam.takoy at yahoo.com (Sam Takoy) wrote: >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}] They both sum for me. In[1]:= 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[1]= (PolyLog[3, (-E^((-I)*a))*r] + PolyLog[3, (-E^(I*a))*r])/2 Out[2]= (PolyLog[3, -E^((-I)*a)] + PolyLog[3, -E^(I*a)])/2 In[3]:= $Version Out[3]= 7.0 for Mac OS X x86 (64-bit) (February 19, 2009)