) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS y(t)有n+2个零点 ∴彐 (n+1) ()=0 (n+1 c(n+1) (2)-k(a)(n+1) k(a)= f(n() (n+1)! 由a的任意性 R,(x)= fm(2) (x-x0)…(x-xn) (n+1)数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS (t) 有n+2个零点 ( 1)! ( ) ( ) ( ) ( ) ( )( 1)! , ( ) 0 ( 1) ( 1) ( 1) ( 1) + = = − +  = + + + + n f k a f k a n n n n n        ( ) ( ) ( 1)! ( ) ( ) 0 ( 1) n n n x x x x n f R x − − +  = +   由a的任意性