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