A class of series acceleration formulae for Catalan's constant

Details A class of series acceleration formulae for Catalan's constant A class of series acceleration formulae for Catalan's constant

2007-06-03

arxiv.org/abs/0706.0356v1

Ramanujan Journal Vol. 3 (1999), no. 2, pp. 159--173. [MR 1703281] (2000f:11163)

Mathematics

Classical Analysis and ODEs

13 pages, AMSLaTeX

Scientific paper

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 pi times the logarithm of an algebraic unit.

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