A Class of Series Acceleration Formulae for Catalan's Constant (1999)
by
David M. Bradley
,
M. Borwein
| Citations: | 7 - 2 self |
BibTeX
@MISC{Bradley99aclass,
author = {David M. Bradley and M. Borwein},
title = {A Class of Series Acceleration Formulae for Catalan's Constant},
year = {1999}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
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 # times the logarithm of an algebraic unit.
