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

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

In:= \$Version

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

```

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