{- Copyright (C) 2011 Dr. Alistair Ward This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. -} {- | [@AUTHOR@] Dr. Alistair Ward [@DESCRIPTION@] Defines the /Gosper/ series; <http://www.pi314.net/eng/goutte.php> -} module Factory.Math.Implementations.Pi.Spigot.Gosper( -- * Constants series ) where import qualified Factory.Math.Implementations.Pi.Spigot.Series as Math.Implementations.Pi.Spigot.Series import qualified Factory.Math.Precision as Math.Precision -- | Defines a series which converges to /Pi/. series :: Integral i => Math.Implementations.Pi.Spigot.Series.Series i series = Math.Implementations.Pi.Spigot.Series.MkSeries { Math.Implementations.Pi.Spigot.Series.baseNumerators = map (\i -> i * pred (2 * i)) [1 ..], Math.Implementations.Pi.Spigot.Series.baseDenominators = map ((* 3) . (\i -> succ i * (i + 2))) [3, 6 ..], Math.Implementations.Pi.Spigot.Series.coefficients = [3, 8 ..], -- 5n - 2 Math.Implementations.Pi.Spigot.Series.nTerms = Math.Precision.getTermsRequired $ 1 / 13 {-empirical convergence-rate-} }