α i ( x ) = [ 1 + 2 ( x i − x ) ∑ k = 0 , k ≠ i n 1 x i − x k ] l i 2 ( x ) \alpha_i(x)=[1+2(x_i- x)\sum_{k=0,k\ne i}^{n}\frac{1}{x_i-x_k}]l_i^2(x) αi(x)=[1+2(xi−x)k=0,k̸=i∑nxi−xk1]li2(x) β i ( x ) = ( x − x i ) l i 2 ( x ) \beta_i(x)=(x-x_i)l_i^2(x) βi(x)=(x−xi)li2(x) 当n=1时 H 3 ( x ) = f ( x 0 ) [ 1 + 2 ( x 0 − x ) x 0 − x 1 ] ( x − x 1 x 0 − x 1 ) 2 + f ( x 1 ) [ 1 + 2 ( x 1 − x ) x 1 − x 0 ] ( x − x 0 x 1 − x 0 ) 2 + f ′ ( x 0 ) ( x − x 0 ) ( x − x 1 x 0 − x 1 ) 2 + f ′ ( x 1 ) ( x − x 1 ) ( x − x 0 x 1 − x 0 ) 2 H_3(x)=f(x_0)[1+2\frac{(x_0-x)}{x_0-x_1}](\frac{x-x_1}{x_0-x_1})^2+ f(x_1)[1+2\frac{(x_1-x)}{x_1-x_0}](\frac{x-x_0}{x_1-x_0})^2+ f'(x_0)(x-x_0)(\frac{x-x_1}{x_0-x_1})^2+ f'(x_1)(x-x_1)(\frac{x-x_0}{x_1-x_0})^2 H3(x)=f(x0)[1+2x0−x1(x0−x)](x0−x1x−x1)2+f(x1)[1+2x1−x0(x1−x)](x1−x0x−x0)2+f′(x0)(x−x0)(x0−x1x−x1)2+f′(x1)(x−x1)(x1−x0x−x0)2