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

Modulemath-functions-0.3.4.4Haskell2010

Numeric.Series

Functions for working with infinite sequences. In particular summation of series and evaluation of continued fractions.

Contents

Data type for infinite sequences.
Constructors
Summation of series
Evaluation of continued fractions

Synopsis

data Sequence
value enumSequenceFrom
value enumSequenceFromStep
value scanSequence
value sumSeries
value sumPowerSeries
value sequenceToList
value evalContFractionB

Packagemath-functions-0.3.4.4
Exports8
LanguageHaskell2010
LicenceBSD-2-Clause
SourceSeries.hs

Data type for infinite sequences.

datadata Sequence a

Infinite series. It's represented as opaque state and step function.

Constructors

forall s. Sequence s (s -> (a, s))

Instances4Functor, Applicative, Fractional, Num

Functor SequenceDefined in math-functions-0.3.4.4 · Numeric.Series
Applicative SequenceDefined in math-functions-0.3.4.4 · Numeric.Series
Fractional a => Fractional (Sequence a)Defined in math-functions-0.3.4.4 · Numeric.Series
Elementwise operations with sequences
Num a => Num (Sequence a)Defined in math-functions-0.3.4.4 · Numeric.Series
Elementwise operations with sequences

Constructors

valueenumSequenceFrom :: Num a => a -> Sequence a

enumSequenceFrom x generate sequence:

a_n = x + n

valueenumSequenceFromStep :: Num a => a -> a -> Sequence a

enumSequenceFromStep x d generate sequence:

a_n = x + nd

valuescanSequence :: (b -> a -> b) -> b -> Sequence a -> Sequence b

Analog of scanl for sequence.

Summation of series

valuesumSeries :: Sequence Double -> Double

Calculate sum of series

\sum_{i=0}^\infty a_i

Summation is stopped when

a_{n+1} < \varepsilon\sum_{i=0}^n a_i

where ε is machine precision (m_epsilon)

valuesumPowerSeries :: Double -> Sequence Double -> Double

Calculate sum of series

\sum_{i=0}^\infty x^ia_i

Calculation is stopped when next value in series is less than ε·sum.

valuesequenceToList :: Sequence a -> [a]

Convert series to infinite list

Evaluation of continued fractions

valueevalContFractionB :: Sequence (Double, Double) -> Double

Evaluate continued fraction using modified Lentz algorithm. Sequence contain pairs (a[i],b[i]) which form following expression:

b_0 + \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3 + \cdots}}}

Modified Lentz algorithm is described in Numerical recipes 5.2 "Evaluation of Continued Fractions"