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Fungrim entry: 7adfd6

abBn ⁣(t)dt=Bn+1 ⁣(b)Bn+1 ⁣(a)n+1\int_{a}^{b} B_{n}\!\left(t\right) \, dt = \frac{B_{n + 1}\!\left(b\right) - B_{n + 1}\!\left(a\right)}{n + 1}
Assumptions:nZ0andaCandbCn \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
TeX:
\int_{a}^{b} B_{n}\!\left(t\right) \, dt = \frac{B_{n + 1}\!\left(b\right) - B_{n + 1}\!\left(a\right)}{n + 1}

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("7adfd6"),
    Formula(Equal(Integral(BernoulliPolynomial(n, t), For(t, a, b)), Div(Sub(BernoulliPolynomial(Add(n, 1), b), BernoulliPolynomial(Add(n, 1), a)), Add(n, 1)))),
    Variables(n, a, b),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(a, CC), Element(b, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-11-19 15:10:20.037976 UTC