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Fungrim entry: 05202b

∫zz+1Bn ⁣(t) dt=zn\int_{z}^{z + 1} B_{n}\!\left(t\right) \, dt = {z}^{n}
Assumptions:n∈Z≥0  and⁡  z∈Cn \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
TeX:
\int_{z}^{z + 1} B_{n}\!\left(t\right) \, dt = {z}^{n}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Integral∫abf(x) dx\int_{a}^{b} f(x) \, dx Integral
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
Powab{a}^{b} Power
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("05202b"),
    Formula(Equal(Integral(BernoulliPolynomial(n, t), For(t, z, Add(z, 1))), Pow(z, n))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(z, CC))))

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2021-03-15 19:12:00.328586 UTC