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A Class of Series Acceleration Formulae for Catalan's Constant

Bradley, David M. (1997) A Class of Series Acceleration Formulae for Catalan's Constant. [Preprint]

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      Abstract

      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 $\pi$ times the logarithm of an algebraic unit.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: log tangent integral, central binomial coefficient, algebraic unit, Catalan's constant
      Subjects: UNSPECIFIED
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/194

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