周期為2π的函數(shù)f(x)為奇函數(shù)時,其傅里葉基數(shù)是正弦級數(shù).
an=1/L∫(-L~L)f(x)cos(nπx/L)dx (n=0,1,2...)
bn=1/L∫(-L~L)f(x)sin(nπx/L)dx (n=1,2,3...)
當f（x）是奇函數(shù)的時候f(x)cos(nπx/L)是奇函數(shù),而且它的定義域關(guān)于y軸對稱,所以此時an=0,f(x)sin(nπx/L)此時為偶函數(shù)
bn=1/L∫(-L~L)f(x)sin(nπx/L)dx (n=1,2,3...)
=2/L∫(0~L)f(x)sin(nπx/L)dx (n=1,2,3...)
f(x)~∑bnsin(nπx/L)
即為正弦級數(shù)