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Fungrim entry: 292d70

B2n ⁣(x)B2n\left|B_{2 n}\!\left(x\right)\right| \le \left|B_{2 n}\right|
Assumptions:nZ0andx[0,1]n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, x \in \left[0, 1\right]
TeX:
\left|B_{2 n}\!\left(x\right)\right| \le \left|B_{2 n}\right|

n \in \mathbb{Z}_{\ge 0} \,\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
ClosedInterval[a,b]\left[a, b\right] Closed interval
Source code for this entry:
Entry(ID("292d70"),
    Formula(LessEqual(Abs(BernoulliPolynomial(Mul(2, n), x)), Abs(BernoulliB(Mul(2, n))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(x, ClosedInterval(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.

2019-08-25 15:30:03.056001 UTC