| Copyright | (c) 2018 Alexandre Rodrigues Baldé |
|---|---|
| License | MIT |
| Maintainer | Alexandre Rodrigues Baldé <alexandrer_b@outlook.com> |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Math.NumberTheory.Zeta.Dirichlet
Description
Dirichlet beta-function.
Documentation
betas :: (Floating a, Ord a) => a -> [a] Source #
Infinite sequence of approximate (up to given precision)
values of Dirichlet beta-function at integer arguments, starting with β(0).
The algorithm previously used to compute β for even arguments was derived
from An Euler-type formula for β(2n) and closed-form expressions for a class of zeta series
by F. M. S. Lima, formula (12), but is now based on the
zetaHurwitz recurrence.
>>>take 5 (betas 1e-14) :: [Double][0.5,0.7853981633974483,0.9159655941772189,0.9689461462593694,0.9889445517411051]
betasEven :: forall a. (Floating a, Ord a) => a -> [a] Source #
Infinite sequence of approximate values of the Dirichlet β function at
positive even integer arguments, starting with β(0).
betasOdd :: [ExactPi] Source #
Infinite sequence of exact values of Dirichlet beta-function at odd arguments, starting with β(1).
>>>approximateValue (betasOdd !! 25) :: Double0.9999999999999987>>>import Data.Number.Fixed>>>approximateValue (betasOdd !! 25) :: Fixed Prec500.99999999999999999999999960726927497384196726751694