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Fungrim entry: 03ee0b

Bn ⁣(12)=(21−n−1)BnB_{n}\!\left(\frac{1}{2}\right) = \left({2}^{1 - n} - 1\right) B_{n}
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
B_{n}\!\left(\frac{1}{2}\right) = \left({2}^{1 - n} - 1\right) B_{n}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
Powab{a}^{b} Power
BernoulliBBnB_{n} Bernoulli number
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("03ee0b"),
    Formula(Equal(BernoulliPolynomial(n, Div(1, 2)), Mul(Sub(Pow(2, Sub(1, n)), 1), BernoulliB(n)))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC