Re: ComplexExpand
- To: mathgroup at smc.vnet.net
- Subject: [mg44321] Re: ComplexExpand
- From: Friedrich Laher <mathefritz at schmieder-laher.de>
- Date: Wed, 5 Nov 2003 10:00:52 -0500 (EST)
- References: <bo7osg$aih$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
thank you, folks,
I meanwhile know it's a bug(?) in my mathematica 4.2 .
Friedrich Laher wrote:
> 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
>
>
>