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Fungrim entry: 4246ae

B2n ⁣(x)<B2n\left|B_{2 n}\!\left(x\right)\right| < \left|B_{2 n}\right|
Assumptions:nZ1andx(0,1)n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, x \in \left(0, 1\right)
TeX:
\left|B_{2 n}\!\left(x\right)\right| < \left|B_{2 n}\right|

n \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, x \in \left(0, 1\right)
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
BernoulliBBnB_{n} Bernoulli number
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
Entry(ID("4246ae"),
    Formula(Less(Abs(BernoulliPolynomial(Mul(2, n), x)), Abs(BernoulliB(Mul(2, n))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(x, OpenInterval(0, 1)))))

Topics using this entry

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

2019-11-19 15:10:20.037976 UTC