# A Class of Series Acceleration Formulae for Catalan's Constant

@article{Bradley1999ACO, title={A Class of Series Acceleration Formulae for Catalan's Constant}, author={D. Bradley}, journal={The Ramanujan Journal}, year={1999}, volume={3}, pages={159-173} }

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… Expand

#### 42 Citations

On a class number formula for real quadratic number fields

- Mathematics
- Bulletin of the Australian Mathematical Society
- 2002

A summation formula for convergence acceleration of some Dirichlet and related series

- Mathematics
- 2006

Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume VI

- Mathematics
- 2007

On Rapidly Convergent Series Expressions for Zeta- and L-Values, and Log Sine Integrals

- Mathematics
- 2001

Integral representations of some series involving (2kk)-1k-1 and some related series

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2004

#### References

SHOWING 1-10 OF 30 REFERENCES

Searching symbolically for Ape´ry-like formulae for values of the Riemann zeta function

- Mathematics, Computer Science
- SIGS
- 1996

Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two

- Mathematics
- 1979

Simplification of Expressions Involving Radicals

- Computer Science, Mathematics
- J. Symb. Comput.
- 1985