A Simple Computation of zeta (2k)

  1. Ciaurri, O. 1
  2. Navas, L.M. 2
  3. Ruiz, F.J. 3
  4. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    GRID grid.11762.33

  3. 3 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    GRID grid.11205.37

Journal:
American Mathematical Monthly

ISSN: 0002-9890

Year of publication: 2015

Volume: 122

Issue: 5

Pages: 444-451

Type: Article

Export: RIS
DOI: 10.4169/amer.math.monthly.122.5.444 SCOPUS: 2-s2.0-85000420383 WoS: 000370067500004 GOOGLE SCHOLAR

Metrics

Cited by

  • Scopus Cited by: 9 (12-06-2021)

Journal Citation Reports

  • Year 2015
  • Journal Impact Factor: 0.349
  • Best Quartile: Q4
  • Area: MATHEMATICS Quartile: Q4 Rank in area: 273/312 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2015
  • SJR Journal Impact: 0.408
  • Best Quartile: Q3
  • Area: Mathematics (miscellaneous) Quartile: Q3 Rank in area: 200/419

CiteScore

  • Year 2015
  • CiteScore of the Journal : 0.7
  • Area: Mathematics (all) Percentile: 35

Abstract

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).