(2)如果f(x)为偶函数,则有 f() 2 +∑ nuX a Cos =1 其中系数a为1()oab (n=0,1,2,…) 证明令z= T l≤x≤l→-优≤≤T, 设f(x)=f()=F(z),F(x)以2m为周期 F(z)=+2(a, cos nz+b, sinn(2)如果f (x)为偶函数, 则有 cos , 2 ( ) 1 0 = = + n n l n x a a f x dx l n x f x l a a l n n = 0 ( )cos 2 其中系数 为 (n = 0,1,2, ) 证明 , l x z 令 = − l x l − z , ( ) ( ) F(z), lz f x f = 设 = F(z)以2为周期. ( cos sin ), 2 ( ) 1 0 a nz b nz a F z n n = + n + =