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Re: Simplifying to PolyLog


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)



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