自然数方幂和的包含Bernoulli数的精确表示式

THE EXPLICIT EXPRESSION INVOLVING BERNOULLI NUMBERS FOR THE POWER SUM OF NATURAL NUMBERS

本文证明自然数方幂和可以用多项式表示,并用两种方法给出其系数包含Bernoulli数的几种精确表示式。

This paper shows that the power sum of natural numbers can be expressed in terms of the multinomial. By using two methods, several explicit expressions involving Bernoulli numbers as coefficients are raised.