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MathGroup Archive 2003

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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




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