Copyright | (c) 2016 Andrew Lelechenko |
---|---|

License | MIT |

Maintainer | Andrew Lelechenko <andrew.lelechenko@gmail.com> |

Stability | Provisional |

Portability | Non-portable (GHC extensions) |

Safe Haskell | Safe |

Language | Haskell2010 |

Riemann zeta-function.

# Documentation

zetas :: (Floating a, Ord a) => a -> [a] Source #

Infinite sequence of approximate (up to given precision)
values of Riemann zeta-function at integer arguments, starting with `ζ(0)`

.
Computations for odd arguments are performed in accordance to
Computational strategies for the Riemann zeta function
by J. M. Borwein, D. M. Bradley, R. E. Crandall, formula (57).

> take 5 (zetas 1e-14) :: [Double] [-0.5,Infinity,1.6449340668482262,1.2020569031595942,1.0823232337111381]

Beware to force evaluation of `zetas !! 1`

, if the type `a`

does not support infinite values
(for instance, `Fixed`

).

zetasEven :: [ExactPi] Source #

Infinite sequence of exact values of Riemann zeta-function at even arguments, starting with `ζ(0)`

.
Note that due to numerical errors convertation to `Double`

may return values below 1:

> approximateValue (zetasEven !! 25) :: Double 0.9999999999999996

Use your favorite type for long-precision arithmetic. For instance, `Fixed`

works fine:

> approximateValue (zetasEven !! 25) :: Fixed Prec50 1.00000000000000088817842111574532859293035196051773