ComplexExpand

*To*: mathgroup at smc.vnet.net*Subject*: [mg44280] ComplexExpand*From*: Friedrich Laher <mathefritz at schmieder-laher.de>*Date*: Tue, 4 Nov 2003 03:23:52 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

It IS TRUE, for integer n > 0 and real x that for s = Sum[Binomial[n,k]Cos[x(n-2k],{k,0,n}] s ==(2 Cos[x])^n but the only way to verify that by mathematica seems to be (s/.n -> m)/(s/.n -> m-1) which results in 2 Cos[x] ComplexExpand[s] does not know that s is real of value (2 Cos[x])^n even if s = Simplify[Sum[Binomial[n,k]Cos[x(n-2k],{k,0,n}], Element[x, Reals] && Element[n,Integers] && n > 0] does not know that s is real of value (2 Cos[x])^n

**Follow-Ups**:**Re: ComplexExpand***From:*Murray Eisenberg <murray@math.umass.edu>

**Re: ComplexExpand***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>