# Question:Fourier serie with variable parameters

## Question:Fourier serie with variable parameters

Maple 14

Hi all,

I have this piecewise function:

Mr := theta->piecewise(theta>=0 and theta<=(Pi/(2*p))-(beta/2),0,theta>(Pi/(2*p))-(beta/2) and theta<=(Pi/(2*p))+(beta/2),Br/mu0,theta>(Pi/(2*p))+(beta/2) and theta<=((3*Pi)/(2*p))-(beta/2),0,theta>((3*Pi)/(2*p))-(beta/2) and theta<=((3*Pi)/(2*p))+(beta/2),-Br/mu0,theta>((3*Pi)/(2*p))+(beta/2) and theta<=2*Pi/p,0);

I want to calculate the Fourier serie of this function without giving the values of Br, mu0, p, beta and alpha. The resulting coefficients are function of those parameters. Is it possible ?

The coefficients could be calculated by those integrals or with commande FourierSeries of maple.

a[n] := (int(Mr(theta)*cos(n*p*theta), theta = 0 .. 2*Pi/p))/(Pi/p);

b[n] := (int(Mr(theta)*sin(n*p*theta), theta = 0 .. 2*Pi/p))/(Pi/p);

I want to get a[n]and b[n] as function of the parameters Br, mu0, p, beta and alpha.

When those values are known, the signal is as follow:

Br:=1.18: mu0:=4*Pi*1e-7: p:=2: beta:=alpha*Pi/p:alpha:=0.5:

plot(Mr(theta),theta=0..2*Pi/p);