The Ramanujan Journal

, Volume 3, Issue 2, pp 159–173

A Class of Series Acceleration Formulae for Catalan's Constant

  • David M. Bradley

DOI: 10.1023/A:1006945407723

Cite this article as:
Bradley, D.M. The Ramanujan Journal (1999) 3: 159. doi:10.1023/A:1006945407723


In this note, we develop transformation formulae and expansions for the log tangent integral, which are then used to derive series acceleration formulae for certain values of Dirichlet L-functions, such as Catalan's constant. The formulae are characterized by the presence of an infinite series whose general term consists of a linear recurrence damped by the central binomial coefficient and a certain quadratic polynomial. Typically, the series can be expressed in closed form as a rational linear combination of Catalan's constant and π times the logarithm of an algebraic unit.

log tangent integral central binomial coefficient algebraic unit Catalan's constant 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • David M. Bradley
    • 1
  1. 1.Department of Mathematics & StatisticsUniversity of MaineOronog

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