请教下，为什么不同形式定义的函数一个可以得到傅里叶级数，另一个不能得到傅里叶级数呢，两个函数看图都是连续的，在线等回复，谢谢，代码请见2楼

l = \[Pi];
a1 = 1;
f[x_] := a1 /; 0 <= x < l;
f[x_] := -a1 /; l <= x < 2 l;
f[x_] := f[x - 2*l] /; x >= 2 l;
f[x_] := f[x + 2*l] /; x <= 0;
A2 = Plot[f[x], {x, -20 l, 20 l}, PlotRange -> {-2, 2}, Frame -> True,
Axes -> True, PlotStyle -> {{Gray}, Thickness[0.008]}]
第二个
l = \[Pi];
a1 = 1;
f[x_] := Which[-l \[LessSlantEqual] x < 0, -a1, 0 <= x < l, a1];
f[x_] := f[x - 2*l] /; x >= l;
f[x_] := f[x + 2*l] /; x <= -l;
a0 = 1/l*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-l\), \(l\)]\(f[
x] \[DifferentialD]x\)\);
a[n_] := 1/l*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-l\), \(l\)]\(f[x]*Cos[
\*FractionBox[\(n*\[Pi]*x\), \(l\)]] \[DifferentialD]x\)\) // Evaluate
b[n_] := 1/l*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-l\), \(l\)]\(f[x]*Sin[
\*FractionBox[\(n*\[Pi]*x\), \(l\)]] \[DifferentialD]x\)\) // Evaluate
k = 30;
ff[x_] := a0/2 + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(k\)]\((a[n]*Cos[
\*FractionBox[\(n*\[Pi]*x\), \(l\)]] + b[n]*Sin[
\*FractionBox[\(n*\[Pi]*x\), \(l\)]])\)\) // Evaluate;
A2 = Plot[{ff[x], f[x]}, {x, -20 l, 20 l}, PlotRange -> {-2, 2},
Frame -> True, Axes -> False,
PlotStyle -> {{Gray, Red}, {Thickness[0.01], Thickness[0.008]}}]

@wshzh1966
求吧主解答