博立叶级数三角函数形式,f(x) cos nx dx,00(n = 0,1,2,...)annxaon元xf(x) =7+bnsinancos21nπxn=1dx,(n = 1,2,3 ...)f(x)sin/傅立叶级数复数形式：81,n元x日Zf(x)edx,L(n=0,±1,±2,..)Cn =f(x) =CneTn=-00-n元xn元xc.LCeX实函数-
𝑓(𝑥) = 𝑎0 2 + 𝑛=1 ∞ 𝑎𝑛cos 𝑛𝜋𝑥 𝑙 + 𝑏𝑛sin 𝑛𝜋𝑥 𝑙 ��− = �𝑎� 𝑙 𝑓(𝑥) cos 𝑛𝜋𝑥 𝑙 𝑑𝑥, (𝑛 = 0,1,2, . . .) 𝑏𝑛 = න −𝑙 𝑙 𝑓(𝑥) sin 𝑛𝜋𝑥 𝑙 𝑑𝑥, (𝑛 = 1,2,3 . ) 傅立叶级数三角函数形式： 傅立叶级数复数形式: 𝑓(𝑥) = 𝑛=−∞ ∞ 𝑐𝑛𝑒 𝑖 𝑛𝜋𝑥 𝑙 𝑐𝑛 = 1 𝑇 න −𝑙 𝑙 𝑓(𝑥) 𝑒 −𝑖 𝑛𝜋𝑥 𝑙 𝑑𝑥, (𝑛 = 0, ±1, ±2, . ) 𝑐𝑛𝑒 𝑖 𝑛𝜋𝑥 𝑙 𝑐−𝑛𝑒 𝑖 −𝑛𝜋𝑥 + 𝑙 = 实函数
博立叶级数三角函数形式f(x) cos nrx dx,00(n = 0,1,2,...)aonxn元xf(x) =+bnsinancos21n元xn=1dx(n = 1,2,3 ..)f(x)sin1傅立叶级数复数形式8n元xn元xZf(x)edx,(n = 0, ±1,±2, ..)Cnf(x) =2Cnen=-00Imag(i)Real0
𝑓(𝑥) = 𝑎0 2 + 𝑛=1 ∞ 𝑎𝑛cos 𝑛𝜋𝑥 𝑙 + 𝑏𝑛sin 𝑛𝜋𝑥 𝑙 ��− = �𝑎� 𝑙 𝑓(𝑥) cos 𝑛𝜋𝑥 𝑙 𝑑𝑥, (𝑛 = 0,1,2, . . .) 𝑏𝑛 = න −𝑙 𝑙 𝑓(𝑥) sin 𝑛𝜋𝑥 𝑙 𝑑𝑥, (𝑛 = 1,2,3 . ) 傅立叶级数三角函数形式： 傅立叶级数复数形式: 𝑓(𝑥) = 𝑛=−∞ ∞ 𝑐𝑛𝑒 𝑖 𝑛𝜋𝑥 𝑙 𝑐𝑛 = 1 𝑇 න −𝑙 𝑙 𝑓(𝑥) 𝑒 −𝑖 𝑛𝜋𝑥 𝑙 𝑑𝑥, (𝑛 = 0, ±1, ±2, . )