Copyright | (c) 2018 Alexandre Rodrigues Baldé |
---|---|

License | MIT |

Maintainer | Alexandre Rodrigues Baldé <alexandrer_b@outlook.com> |

Safe Haskell | Safe |

Language | Haskell2010 |

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.

`>>>`

[0.5,0.7853981633974483,0.9159655941772189,0.9689461462593694,0.9889445517411051]`take 5 (betas 1e-14) :: [Double]`

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)`

.

`>>>`

0.9999999999999987`approximateValue (betasOdd !! 25) :: Double`

`>>>`

`import Data.Number.Fixed`

`>>>`

0.99999999999999999999999960726927497384196726751694`approximateValue (betasOdd !! 25) :: Fixed Prec50`