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Re: Simplifying to PolyLog

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113520] Re: Simplifying to PolyLog
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 1 Nov 2010 04:59:37 -0500 (EST)

Appears to be version dependent

$Version

"7.0 for Mac OS X x86 (64-bit) (February 19, 2009)"

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

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

Sum[(-1)^n Cos[a n]/n^3,
 {n, 1, Infinity}]

(1/2)*(PolyLog[3, -E^((-I)*a)] + 
      PolyLog[3, -E^(I*a)])


Bob Hanlon

---- Sam Takoy <sam.takoy at yahoo.com> wrote: 

=============
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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