Fourierovy řady

f(x)=(∑_( k=0)^∞)(Subscript[a, k])cos((k π x)/l)+(∑_( k=1)^∞)(Subscript[b, k])sin((k π x)/l)

f(x)=((Subscript[a, 0])/2)+(∑_( k=1)^∞)(a^k)cos((k π x)/l)+(Subscript[b, k])sin((k π x)/l)

(Subscript[a, k])=(1/l)(∫_0^(2l))f(x)cos((k π x)/l)dx     k=0,1,...
(Subscript[b, k])=(1/l)(∫_0^(2l))f(x)sin((k π x)/l)dx     k=1,2,...

<<"FourierSeries`"

f(x)=x, x ∈ [0,2π)

f[x_]=Piecewise[{{x+2Pi,x<=0},{x,x>0}}]

Plot[f[x],{x,-2Pi,2Pi}]

FourierTrigSeries[f[x],x,20,FourierParameters->{0,1/(4Pi)}]

Simplify[%]

f(x)=1(x)-1(-x), x ∈ [-π,π)

f[x_]=UnitStep[x]-UnitStep[-x]

Plot[f[x],{x,-Pi,Pi}]

FourierTrigSeries[f[x],x,10,FourierParameters->{0,1/(2Pi)}]

Simplify[%]

Expand[%]

f(x)=|x|, x ∈ [-π,π)

f[x_]=Abs[x]

Plot[f[x],{x,-Pi,Pi}]

FourierTrigSeries[f[x],x,10,FourierParameters->{0,1/(2)}]

Simplify[%]