江画工太猩院 假设P(x)=f“(x)k=12,…,n n,=f(x),1a1=f(x),2a2=f"(x) ……,na,=f"(x) 得 f(x)(k=0,2,…,n) k 代入P(x)中得 P2(x)=f(xn)+f(xn)(x-x)+(x-x0)2+ e(n) + x=x江西理工大学理学院 假设 P x f x k n k k n ( ) ( ) 1,2, , 0 ( ) 0 ( ) = = L ( ), 0 0 a = f x 代入P ( x) n 中得 n n n x x n f x x x f x P x f x f x x x ( ) !( ) ( ) 2!( ) ( ) ( ) ( )( ) 0 0 ( ) 2 0 0 0 0 0 + − − + ′′ = + ′ − + L 得 ( ) ( 0,1,2, , ) !1 0 ( ) f x k n k a k k = = L 1 ( ), 1 x0 ⋅ a = f ′ 2! ( ) 2 0 ⋅a = f ′′ x L L , ! ( )0 ( ) n a f x n ⋅ n =