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Re: ComplexExpand


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


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