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Fungrim entry: 555e10

Bn ⁣(x)=∑k=0n(nk)Bn−kxkB_{n}\!\left(x\right) = \sum_{k=0}^{n} {n \choose k} B_{n - k} {x}^{k}
Assumptions:n∈Z≥0 and⁡ x∈Cn \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
B_{n}\!\left(x\right) = \sum_{k=0}^{n} {n \choose k} B_{n - k} {x}^{k}

n \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
Binomial(nk){n \choose k} Binomial coefficient
BernoulliBBnB_{n} Bernoulli number
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("555e10"),
    Formula(Equal(BernoulliPolynomial(n, x), Sum(Mul(Mul(Binomial(n, k), BernoulliB(Sub(n, k))), Pow(x, k)), Tuple(k, 0, n)))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(x, CC))))

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2019-06-18 07:49:59.356594 UTC