A Simple Computation of ζ (2k)

被引：6

作者：

Ciaurri, Oscar ^{[1
]}

Navas, Luis M. ^{[2
]}

Ruiz, Francisco J. ^{[3
]}

Varona, Juan L. ^{[1
]}

机构：

[1] Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain

[2] Univ Salamanca, Dept Matemat, E-37008 Salamanca, Spain

[3] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

来源：

AMERICAN MATHEMATICAL MONTHLY | 2015年 / 122卷 / 05期

关键词：

EULERS FORMULA; ELEMENTARY PROOF;

D O I：

10.4169/amer.math.monthly.122.5.444

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a new simple proof of Euler's formulas for zeta(2k), where k = 1, 2, 3,.... The computation is done using only the defining properties of the Bernoulli polynomials and summing a telescoping series. The same method also yields integral formulas for zeta(2k + 1).

引用

页码：444 / 451

页数：8

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