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Fungrim entry: e89eb5

ddx Bn ⁣(x)=nBn−1 ⁣(x)\frac{d}{d x}\, B_{n}\!\left(x\right) = 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:
\frac{d}{d x}\, B_{n}\!\left(x\right) = 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
Derivativeddz f ⁣(z)\frac{d}{d z}\, f\!\left(z\right) 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(Derivative(BernoulliPolynomial(n, x), Tuple(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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2019-06-18 07:49:59.356594 UTC