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MathGroup Archive 2003

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Re: ComplexExpand

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44313] Re: [mg44280] ComplexExpand
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 5 Nov 2003 10:00:36 -0500 (EST)
  • References: <200311040823.DAA10495@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 4 Nov 2003, at 17:23, 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
>
>
>
>
>

My Mathematica 5.0 returns


Sum[Binomial[n, k]*Cos[x*(n - 2*k)], {k, 0, n}]


2^n*Cos[x]^n

??

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/


  • References:
    • ComplexExpand
      • From: Friedrich Laher <mathefritz@schmieder-laher.de>
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