多项式的特征

CHARACTERIZATIONS OF POLYNOMIALS

是ｆ（ｘ）的ｎ－１阶差商．不需要任何解析的假设，我们给出方程的一般解，解决了１９９２年Ｂａｉｌｅｙ提出的问题．另外，我们也给出两个其他多项式特征．

Let f [x1,x2, …,xn] be the divided difference of f(x) on n-1 points. Wedetermine the general solution ofwithout any regularity asumption. This answers a question raised by Bailey in 1992[4]Furthermore, we give two other characterizations of polynomials.