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)+(b^k)sin((k π x)/l)

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

<< Calculus`FourierTransform`

FourierTrigSeries[x, {x, 0, 2  Pi}, 10]

FourierTrigSeries[UnitStep[x] - UnitStep[-x], {x, -Pi, Pi}, 10]

FourierTrigSeries[Abs[x], {x, -1, 1}, 10]

FourierTrigSeries[x, {x, -1, 1}, 10]

FourierTrigSeries[x  x, {x, -2 Pi, 2  Pi}, 10]

FourierExpSeries[x, {x, -1, 1}, 5]