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}
}
  • D. Bradley
  • Published 1999
  • Mathematics
  • The Ramanujan Journal
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
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