Subject: Stripping out coefficients of Fourier series
From: Dan Hatton
Date: Tue, 2 Jun 2009 17:46:54 +0100 (BST)
On Mon, 1 Jun 2009, Dan Hatton wrote:
> Imagine I have some three-dimensional Fourier series like
> series : (complicated_expression_1)*cos(3*z)*cos(3*x)*cos(y)
> +(complicated_expression_2)*cos(2*z)*cos(2*x)*cos(2*y) ;
> (only with rather more than two Fourier components).
> complicated_expression_1 and complicated_expression_2 are free of x,
> y, and z.
> I know the Fourier series is zero for all (x,y,z) - from which I infer
> that complicated_expression_1 and complicated_expression_2 are zero
> individually. So I'd like to do some algebraic manipulations with the
> equations
> complicated_expression_1 = 0 ;
> complicated_expression_2 = 0 ;
> but first I have to be able to extract complicated_expression_1 and
> complicated_expression_2 from series. Is there a Maxima function I
> can apply to series to achieve this, please?
Oh, what a fool I am... I just realized I can take advantage of the
orthogonality of the Fourier components, so the following should do
the job, albeit at the expense of quite a bit of CPU time:
integrate(integrate(integrate(series*cos(3*x)*cos(y)*cos(3*z),z,0,2*%pi),y,0,2*%pi),x,0,2*%pi)/%pi^2 = 0 ;
integrate(integrate(integrate(series*cos(2*x)*cos(2*y)*cos(2*z),z,0,2*%pi),y,0,2*%pi),x,0,2*%pi)/%pi^2 = 0 ;
But thanks for the other tip, Joshua.
--
Regards,
Dan