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Fungrim entry: e89eb5

Bn′(x)=nBn−1 ⁣(x)B'_{n}(x) = n B_{n - 1}\!\left(x\right)
Assumptions:n∈Z≥1  and⁡  x∈Cn \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
TeX:
B'_{n}(x) = n B_{n - 1}\!\left(x\right)

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddz f ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("e89eb5"),
    Formula(Equal(ComplexDerivative(BernoulliPolynomial(n, x), For(x, x, 1)), Mul(n, BernoulliPolynomial(Sub(n, 1), x)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(1)), Element(x, CC))))

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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