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MathGroup Archive 2003

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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
> 
> 
> 


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