Math.Algebra.Polynomial.Univariate.Bernoulli

Bernoulli and Euler polynomials

See https://en.wikipedia.org/wiki/Bernoulli_polynomials

Documentation

bernoulliB :: (Field c, KnownSymbol v) => Int -> Univariate c v

Bernoulli polynomials

eulerE :: (Field c, KnownSymbol v) => Int -> Univariate c v

Euler polynomials (not to be confused with the related Eulerian polynomials!)

rationalBernoulliB :: Int -> Univariate Rational "x"

rationalEulerE :: Int -> Univariate Rational "x"

bernoulliNumber :: Integral a => a -> Rational

Bernoulli numbers. bernoulli 1 == -1%2 and bernoulli k == 0 for k>2 and odd. This function uses the formula involving Stirling numbers of the second kind. Numerators: A027641, denominators: A027642.

signedEulerNumber :: Int -> Integer

Signed Euler numbers (unsigned version: A000364)

See https://en.wikipedia.org/wiki/Euler_number

NOTE: we skip the zeros (every other index)

unsignedEulerNumber :: Int -> Integer

unsigned Euler numbers (A000364)

NOTE: we skip the zeros (every other index)

eulerianPolynomial :: Int -> Univariate Integer "x"

Eulerian polynomials (row polynomials of A060187)