A Class of Series Acceleration Formulae for Catalan's Constant
- Cite this article as:
- Bradley, D.M. The Ramanujan Journal (1999) 3: 159. doi:10.1023/A:1006945407723
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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.