$d_1$

$d_2$

$f(d_1)$

$f(d_2)$

$f(d_0)$

$f(d_3)$

$\textcolor{#006400}{f_1(x)=}$

$\textcolor{#CC0000}{f_2(x)=}$

$\textcolor{#0000FF}{f_3(x)=}$

$f_{i}$

$d_3$

$d_0$

\text{Fourierkoeffizienten:}

$d_1=$

$d_2=$

\text{(Stückweise definierte) Funktion:}

P_{text}: Corner[2, 4] + (1, -6)
k = 0 (slider from 0 to 30, step 1)
d_2: 5
d_1: 3
f_3(x) = (-1.56 * (x - 5)) + 2
f_2(x) = (2 * (1 - (x - 4)^(2))) + 2
f_1(x) = (((x - 3) * (x - 2)) * (x - 1) / 3) + 2
f(x) = If[x ≥ 0 ∧ x < d_1, f_1(x), If[x ≥ d_1 ∧ x < d_2, f_2(x), If[x ≥ d_2 ∧ x ≤ (2 * π), f_3(x)]]]
a = Sequence((1 / π * (Integral[(f_1(x) * cos((n * x))), 0, d_1] + Integral[(f_2(x) * cos((n * x))), d_1, d_2] + Integral[(f_3(x) * cos((n * x))), d_2, (2 * π)])), n, 0, 30)
D_1: (d_1, 0)
D_2: (d_2, 0)
F_1: D_1 + (0, f(D_1))
F_2: D_2 + (0, f(D_2))
F_0: (0, f(0))
F_3: ((2 * π), f((2 * π)))
inputF1 = Textfield(f_1)
inputF2 = Textfield(f_2)
inputF3 = Textfield(f_3)
b = Sequence((1 / π * (Integral[(f_1(x) * sin((n * x))), 0, d_1] + Integral[(f_2(x) * sin((n * x))), d_1, d_2] + Integral[(f_3(x) * sin((n * x))), d_2, (2 * π)])), n, 1, 30)
f_{i}(x) = (1 / 2 * Element[a, 1]) + If[k > 0, Sum[(Element[a, n + 1] * cos((n * x))) + (Element[b, n] * sin((n * x))), n, 1, k], 0]
g_1: x = x(D_1)
g_2: x = x(D_2)
D_3: ((2 * π), 0)
D_0: (0, 0)
textA = Sequence(Text["a_{" + (i) + "}=" + (Element[a, i + 1]), P_{text} - (0, (i * 0.5)), true, true], i, 0, k)
textB = Sequence(Text["b_{" + (i + 1) + "}=" + (Element[b, i + 1]), P_{text} - (-2.5, ((i + 1) * 0.5)), true, true], i, 0, k - 1)
textB_{2} = If(k > 10, Append[Take[textB, 1, 10], Text["...", P_{text} - (-2.5, 5.5), true, true]], textB)
textA_{2} = If(k > 10, Append[Take[textA, 1, 11], Text["...", P_{text} - (0, (11 * 0.5)), true, true]], textA)
inputD1 = Textfield(d_1)
inputD2 = Textfield(d_2)