# Fungrim entry: e89eb5

$B'_{n}(x) = n B_{n - 1}\!\left(x\right)$
Assumptions:$n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}$
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
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
BernoulliPolynomial$B_{n}\!\left(z\right)$ Bernoulli polynomial
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ 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))))

## Topics using this entry

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