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

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