p(xy, (x)P(x)dx=tp(x)f(x)%(x)dx 内积定义 ( 8)= p(x)f(x)g(x)dx /2=(x)=02=√∫ p(x)(f(x)-0)2dx 于 是 有 ∑(k29,1=(,9)(=0,1,…m) (9)(,9)…(99)a( (19)(,)…(9,9)‖a_(, (0n)(0n,1)…(n2n)0 ( ) ( ) ( ) d ( ) ( ) ( ) d n b b j j k k a a j a x x x x x f x x x      =  =   内积定义 f g x f x g x x b a ( , )  ( ) ( ) ( )d  = 2 2 2 2 2 2 ( ) 0 [ ( )( ( ) 0) d ] ( , ) b a f f x x f x x f f = − = − =   于是有 ( , ) ( , ) ( 0, 1, , ) 0 k j a j f k k n n j  = =  =    . 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) n n n n n n n n a f a f a f                                        =                  