On families of linear recurrence relations for the special values of the Riemann zeta function

被引：7

作者：

Merca, Mircea ^{[1
]}

机构：

[1] Univ Craiova, Dept Math, Craiova 200585, DJ, Romania

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 170卷

关键词：

Bernoulli numbers; Bernoulli polynomials; Riemann zeta function; Recurrences; ELEMENTARY PROOF; EULERS FORMULA;

D O I：

10.1016/j.jnt.2016.06.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we use the generating function of the Bernoulli polynomials to introduce a number of infinite families of linear recurrence relations for the Riemann zeta function at positive even integer arguments, zeta(2n). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：55 / 65

页数：11

共 23 条

[1]

Abramowitz M., 1972, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables

[2]

[Anonymous], 1975, Math. Mag.

[3]

[Anonymous], 1971, Math. Mag.

[4]

[Anonymous], 1953, The American Mathematical Monthly

[5]

Apostol T.M., 1976, INTRO ANAL NUMBER TH

[6] ANOTHER ELEMENTARY PROOF OF EULERS FORMULA FOR ZETA (2N) [J].

APOSTOL, TM .

AMERICAN MATHEMATICAL MONTHLY, 1973, 80 (04) :425-431

[7] EULER AND ZETA-FUNCTION [J].

AYOUB, R .

AMERICAN MATHEMATICAL MONTHLY, 1974, 81 (10) :1067-1086

[8] Computational strategies for the Riemann zeta function [J].

Borwein, JM ;

Bradley, DM ;

Crandall, RE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 121 (1-2) :247-296

[9]

Chen X., 1995, COLL MATH J, V26, P372

[10]

Coffey M.W., ARXIV160101673

← 1 2 3 →