例3求y=x!的一阶差分，二阶差分 解yx=yx+1-yx =(x+1)-x! =x·x! 2y=A(Ay)=A(x·x) =(x+1)(x+-xx =(x2+x+1e: 经济数学 微积分 解 = (x + 1)!−x! 例3求y = x! 的一阶差分，二阶差分. x x x y = y − y +1 = x  x! ( ) ( !) 2  yx =  yx =  x  x = (x +1)(x +1)!−x x! ( 1) ! 2 = x + x + x