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GHC 10.0.0.20260917 · lts/ghc-10.0.x · 8fef28d · 2026-11-02

Modulenumeric-prelude-0.4.4Haskell98

MathObj.PowerSeries.Example

Contents
  1. Default implementations.
  2. Generate Taylor series explicitly.
  3. Power series of (1+x)^expon using the binomial series.
  4. Generate Taylor series from differential equations.
Synopsis
Example6 expressions
import qualified MathObj.PowerSeries.Core as PSimport qualified MathObj.PowerSeries.Example as PSEimport Test.NumericPrelude.Utility (equalTrunc)import NumericPrelude.Numeric as NPimport NumericPrelude.Base as Pimport Prelude ()

Default implementations.

valueexp :: C a => [a]
#
valuesin :: C a => [a]
#
valuecos :: C a => [a]
#
valuetan :: (C a, C a) => [a]
#
valuelog :: C a => [a]
#
valuepow :: C a => a -> [a]
Source#
Property
\m n -> equalTrunc 30 (PS.mul (PSE.pow m) (PSE.pow n)) (PSE.pow (m+n))

Generate Taylor series explicitly.

valueexpExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.expExpl PSE.expODE
valuesinExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.sinExpl PSE.sinODE
valuecosExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.cosExpl PSE.cosODE
valuetanExpl :: (C a, C a) => [a]
Source#
Property
equalTrunc 50 PSE.tanExpl PSE.tanODE
valuetanExplSieve :: (C a, C a) => [a]
Source#
Property
equalTrunc 50 PSE.tanExpl PSE.tanExplSieve
valuelogExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.logExpl PSE.logODE
valueatanExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.atanExpl PSE.atanODE
valuesinhExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.sinhExpl PSE.sinhODE
valuecoshExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.coshExpl PSE.coshODE
valueatanhExpl :: C a => [a]
Source#
Property
equalTrunc 500 PSE.atanhExpl PSE.atanhODE

Power series of (1+x)^expon using the binomial series.

valuepowExpl :: C a => a -> [a]
Source#
Property
\expon -> equalTrunc 50 (PSE.powODE expon) (PSE.powExpl expon)
valuesqrtExpl :: C a => [a]
Source#
Property
equalTrunc 100 PSE.sqrtExpl PSE.sqrtODE
valueerf :: C a => [a]
Source#

Power series of error function (almost). More precisely erf = 2 / sqrt pi * integrate (x -> exp (-x^2)) , with erf 0 = 0.

Generate Taylor series from differential equations.

valuetanODESieve :: C a => [a]
Source#
Property
equalTrunc 50 PSE.tanODE PSE.tanODESieve
valueasinODE :: C a => [a]
Source#
Property
equalTrunc 50 PSE.asinODE (snd $ PS.inv PSE.sinODE)