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

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

  3. 3 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Journal:
American Mathematical Monthly

ISSN: 0002-9890

Year of publication: 2015

Volume: 122

Issue: 5

Pages: 444-451

Type: Article

DOI: 10.4169/AMER.MATH.MONTHLY.122.5.444 SCOPUS: 2-s2.0-85000420383 WoS: WOS:000370067500004 GOOGLE SCHOLAR

More publications in: American Mathematical Monthly

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).