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Fungrim entry: 050c46

Bn=1ek=0knk!B_{n} = \frac{1}{e} \sum_{k=0}^{\infty} \frac{{k}^{n}}{k !}
Assumptions:nZ0n \in \mathbb{Z}_{\ge 0}
B_{n} = \frac{1}{e} \sum_{k=0}^{\infty} \frac{{k}^{n}}{k !}

n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
ConstEee The constant e (2.718...)
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(Equal(BellNumber(n), Mul(Div(1, ConstE), Sum(Div(Pow(k, n), Factorial(k)), For(k, 0, Infinity))))),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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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