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Re: ComplexExpand
*To*: mathgroup at smc.vnet.net
*Subject*: [mg44322] Re: [mg44280] ComplexExpand
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Wed, 5 Nov 2003 10:00:54 -0500 (EST)
*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst
*References*: <200311040823.DAA10495@smc.vnet.net>
*Reply-to*: murray at math.umass.edu
*Sender*: owner-wri-mathgroup at wolfram.com
In Mathematica 5.0:
Sum[Binomial[n, k]Cos[x(n - 2k)], {k, 0, n}]
2^n*Cos[x]^n
(where the output abov is shown in its equivalent InputForm).
Note that you omitted a closing parentheses below in the argument to Cos.
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
>
>
>
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
**References**:
**ComplexExpand**
*From:* Friedrich Laher <mathefritz@schmieder-laher.de>
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