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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