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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 35, Issue 1


Certain identities, connection and explicit formulas for the Bernoulli and Euler numbers and the Riemann zeta-values

Semyon Yakubovich
  • Department of Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, 4169-007 Porto, Portugal
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Published Online: 2015-02-06 | DOI: https://doi.org/10.1515/anly-2014-1286


Various new identities, recurrence relations, integral representations, connection and explicit formulas are established for the Bernoulli and Euler numbers and the values of Riemann's zeta function ζ(s). To do this, we explore properties of some Sheffer's sequences of polynomials related to the Kontorovich–Lebedev transform.

Keywords: Bernoulli polynomials; Bernoulli numbers; Euler polynomials; Euler numbers; generalized Euler polynomials; Sheffer sequences; Von Staudt–Clausen theorem; Riemann zeta function; modified Bessel functions; Kontorovich–Lebedev transform

MSC: 11B68; 11B73; 11B83; 11M06; 12E10; 33C10; 44A15

About the article

Received: 2014-09-29

Revised: 2014-11-27

Accepted: 2015-01-30

Published Online: 2015-02-06

Published in Print: 2015-03-01

Citation Information: Analysis, Volume 35, Issue 1, Pages 59–71, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2014-1286.

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