The Ramanujan Journal

, Volume 46, Issue 1, pp 77–89 | Cite as

On a new constant related to Euler’s constant

Article
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Abstract

This paper introduces a new constant \(\kappa \), with a definition closely related to that of the Euler–Mascheroni’s constant \(\gamma \). Some integrals and infinite sums are evaluated in terms of \(\kappa \).

Keywords

Euler–Mascheroni constant Zeta function Classical analysis Gamma function 

Mathematics Subject Classification

11M99 

References

  1. 1.
    Abramovitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, p. 229. Dover, New York. ISBN 0-486-61272-4 (1964)Google Scholar
  2. 2.
    Guillera, J., Sondow, J.: Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent. Ramanujan J. 16, 247–270 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Lagarias, J.C.: Euler’s constant: Euler’s work and modern developments. Bull. Am. Math. Soc. 50(4), 527–628 (2013)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Sampedro, J.C.: Some unit square integrals. Ramanujan J. 40, 541–555 (2016)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Sondow, J.: Double integrals for Euler’s constant and ln 4/pi and an analog of Hadjicostas’s formula. Am. Math. Mon. 112, 61–65 (2005)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsUPV/EHU-University of Basque CountryLeioaSpain

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