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MathGroup Archive 2005

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Re: Periodic function Roots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58401] Re: Periodic function Roots
  • From: dh <dh at metrohm.ch>
  • Date: Fri, 1 Jul 2005 02:01:54 -0400 (EDT)
  • References: <da0bka$fkj$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
do I understand your question right?
You want to get expansion coefficients A,B,.. in a cosine expansion of 
the periodic function K.
Toward this aim, there is:

Calculus`FourierTransform`FourierCosCoefficient

here is an example: Let K= Mod[t^2,2 Pi] then we get the n-th expansion 
coefficient by:

FourierCosCoefficient[Mod[t^2, 2Pi], t, n]

the first few are: {1/12, -Pi^(-2), 1/(4*Pi^2),
  -1/(9*Pi^2)}

sincerely, Daniel

FBellas wrote:
> Hello, I'm trying to solve an periodic ecuation involving several harmonics
> (Style ACos(x)+BCos(2x)+...==K). Mathematica can't let me us  'Solve'
> function, so it gives me the error:
> Solve::tdep: The equations appear to involve the variables to be solved for
> \
> in an essentially non-algebraic way.
> 
> To arrange this, i'm making a little program involving FindRoot function to
> find at least two roots from the ecuation in the first period. But I would
> like to know if there are some other method to do this more easily.
> 
> Thanks a lot
> 
> F. Bellas
> 
> 
> 
> 
> 
> 


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