1999/06/01 by David M. Bradley · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Coding theory and cryptography #math.CA #math.NT #msc:11M06 #msc:11Y60
paper · pdf · doi:10.1023/a:1006945407723
published as Ramanujan Journal Vol. 3 (1999), no. 2, pp. 159--173. [MR 1703281] (2000f:11163) · 13 pages, AMSLaTeX
openalex publication_date 1999/06/01 · arxiv created 2007/06/03 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.