BernoulliPolynomial

The Bernoulli polynomial $B_n(x)$ -- Wolfram's own BernoulliB(n, x).

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimBernoulliPolynomial✓↗Fungrim entryWolfram LanguageBernoulliB✓↗

BernoulliPolynomial(n, x)exact for a symbolic or exact x, numeric via BernoulliB's own kernel otherwise

mpmathbernpoly(n, x)Juliaenumeratio_bernoulli_poly(n, x)

Typed signatures

Type	Package	Applies
(integer, number) -> number	analytic	always

Domain: Wolfram

Plot

Examples

Basic #

$B_0(x) = 1$

live ↗

In$\mathrm{BernoulliPolynomial}(0, x)$Out$1$

$B_1(x) = x - 1/2$

live ↗

In$\mathrm{BernoulliPolynomial}(1, x)$Out$x-\frac{1}{2}$

Scope #

$B_2(0) = 1/6$

live ↗

In$N(\mathrm{BernoulliPolynomial}(2, 0))$Out$0.166\,666\,666\,666\,666\,66$

$B_2(1) = 1/6$

live ↗

In$N(\mathrm{BernoulliPolynomial}(2, 1))$Out$0.166\,666\,666\,666\,666\,66$

About

Examples	4
Checked against	Wolfram Language 4 agreempmath 2 agreeJulia 2 agree
Crosswalk	FungrimFungrim entry ×11Wolfram LanguagempmathJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts

See also: BernoulliB