{- 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 a <http://en.wikipedia.org/wiki/Srinivasa_Ramanujan>-type series for /Pi/. -} module Factory.Math.Implementations.Pi.Ramanujan.Series( -- * Types -- ** Data-types Series(..) ) where import qualified Data.Ratio import qualified Factory.Math.Precision as Math.Precision -- | Defines a series corresponding to a specific /Ramanujan/-formula. data Series squareRootAlgorithm factorialAlgorithm = MkSeries { terms :: factorialAlgorithm -> [Data.Ratio.Rational], -- ^ The sequence of terms, the sum to infinity of which defines the series. getSeriesScalingFactor :: squareRootAlgorithm -> Math.Precision.DecimalDigits -> Data.Ratio.Rational, -- ^ The ratio by which the sum to infinity of the sequence, must be scaled to result in /Pi/. convergenceRate :: Math.Precision.ConvergenceRate -- ^ The expected number of digits of /Pi/, per term in the series. }