The generalization of Faulhaber's formula to sums of non-integral powers

被引：16
|
作者：
McGown, Kevin J.
Parks, Harold R. [1 ]
机构：
[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 USA
[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 330卷 / 01期
关键词：
sums of non-integral powers; Faulhaber's formula; Bernoulli numbers; Euler-Maclaurin summation; Riemann zeta function;
D O I：
10.1016/j.jmaa.2006.08.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A formula for the sum of any positive-integral power of the first N positive integers was published by Johann Faulhaber in the 1600s. In this paper, we generalize Faulhaber's formula to non-integral complex powers with real part greater than -1. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：571 / 575
页数：5
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