A class of series acceleration formulae for Catalan's constant

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.

13 pages, AMSLaTeX

Cited by in corpus (13)

• Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• Several combinatorial identities derived from series expansions of powers of arcsine
• Some infinite series involving the Riemann zeta function
• Yet Another Table of Integrals
• Evaluation of Log-tangent Integrals by series involving $\zeta (2n+1)$
• Relating log-tangent integrals with the Riemann zeta function
• Note On the Irrationality of the L-Function Constants L(s, X)
• Identities inspired by the Ramanujan Notebooks, second series
• On a class number formula for real quadratic number fields
• Spherical Couplings and Multiple Elliptic Integrals
• Rapidly Convergent Series of the Divisors Functions
• Multiple-Correction and Continued Fraction Approximation