⑩天掌 Teaching Plan on Advanced Mathematics o (2)如果(x)为偶函数则有 f(x)="+∑ a. cOS nTo n=1 其中系数a为n-=2 nTx x)cOS (n=0,,2,…) 证明△,_πx ,一l≤x≤l→-兀≤z≤π 设f(x)=f()=F(z),F(z)以2m为周期 T F(3)=+2(an cos nz+b, sin nz), tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics (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 +  =