The Lerch transcendent from the point of view of Fourier analysis

  1. Navas, L.M. 1
  2. Ruiz, F.J. 2
  3. Varona, J.L. 3
  1. 1 Universidad de Salamanca

    Universidad de Salamanca

    Salamanca, España

    GRID grid.11762.33

  2. 2 Universidad de Zaragoza

    Universidad de Zaragoza

    Zaragoza, España

    GRID grid.11205.37

  3. 3 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Year of publication: 2015

Volume: 431

Issue: 1

Pages: 186-201

Type: Article

Export: RIS
DOI: 10.1016/j.jmaa.2015.05.048 SCOPUS: 2-s2.0-84937639634 WoS: 000357441100013 GOOGLE SCHOLAR


Cited by

  • Scopus Cited by: 2 (12-06-2021)

Journal Citation Reports

  • Year 2015
  • Journal Impact Factor: 1.014
  • Best Quartile: Q1
  • Area: MATHEMATICS Quartile: Q1 Rank in area: 56/312 (Ranking edition: SCIE)
  • Area: MATHEMATICS, APPLIED Quartile: Q2 Rank in area: 88/254 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2015
  • SJR Journal Impact: 1.15
  • Best Quartile: Q1
  • Area: Applied Mathematics Quartile: Q1 Rank in area: 100/545
  • Area: Analysis Quartile: Q2 Rank in area: 36/133


  • Year 2015
  • CiteScore of the Journal : 2.1
  • Area: Analysis Percentile: 74
  • Area: Applied Mathematics Percentile: 63


We obtain some well-known expansions for the Lerch transcendent and the Hurwitz zeta function using elementary Fourier analytic methods. These Fourier series can be used to analytically continue the functions and prove the classical functional equations, which arise from the relations satisfied by the Fourier conjugate and flat Fourier series. In particular, the functional equation for the Riemann zeta function can be obtained in this way without contour integrals. The conjugate series for special values of the parameters yields analogous results for the Bernoulli and Apostol-Bernoulli polynomials. Finally, we give some consequences derived from the Fourier series. © 2015 Elsevier Inc.