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

页码：571 / 575

页数：5

共 6 条

[1] Averaging sums of powers of integers and Faulhaber polynomials
Luis Cereceda, Jose
ANNALES MATHEMATICAE ET INFORMATICAE, 2013, 42 : 105 - 117
[2] Conjectures Involving a Generalization of the Sums of Powers of Integers
Svinin, Andrei K.
EXPERIMENTAL MATHEMATICS, 2018, 27 (04) : 437 - 443
[3] On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials
Dagli, M. Cihat
Can, Mumun
JOURNAL OF NUMBER THEORY, 2015, 156 : 105 - 124
[4] A FORMULA FOR THE HURWITZ ZETA FUNCTION, RIEMANN'S FUNCTIONAL EQUATION AND CERTAIN INTEGRAL REPRESENTATIONS
Kachi, Yasuyuki
Tzermias, Pavlos
TSUKUBA JOURNAL OF MATHEMATICS, 2018, 42 (02) : 309 - 334
[5] Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of Pi
Qi, Feng
DEMONSTRATIO MATHEMATICA, 2022, 55 (01) : 710 - 736
[6] On the mean value formula for the non-symmetric form of the approximate functional equation of ζ2(s) in the critical strip
Kiuchi, I
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2001, 58 (1-2): : 109 - 119

← 1 →