Copyright | (c) 2018 Alexandre Rodrigues Baldé |
---|---|
License | MIT |
Maintainer | Alexandre Rodrigues Baldé <alexandrer_b@outlook.com> |
Stability | Provisional |
Portability | Non-portable (GHC extensions) |
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 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).
> take 5 (betas 1e-14) :: [Double] [0.5,0.7853981633974483,0.9159655941772191,0.9689461462593693,0.988944551741105]
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) :: Double 0.9999999999999987
Using Fixed
:
> approximateValue (betasOdd !! 25) :: Fixed Prec50 0.99999999999999999999999960726927497384196726751694z