A new method for investigating Euler sums

被引：20

作者：

Basu, A ^{[1
]}

Apostol, TM ^{[1
]}

机构：

[1] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

RAMANUJAN JOURNAL | 2000年 / 4卷 / 04期

关键词：

Riemann zeta function; Euler sums; recursion formulas;

D O I：

10.1023/A:1009868016412

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Euler discovered a recursion formula for the Riemann zeta function evaluated at the even integers. He also evaluated special Dirichlet series whose coefficients are the partial sums of the harmonic series. This paper introduces a new method for deducing Euler's formulas as well as a host of new relations, not only for the zeta function but for several allied functions.

引用

页码：397 / 419

页数：23

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