Fungrim entry: aab4e3

\sum_{n=0}^{\infty} \frac{B_{n}}{n !} {x}^{n} = \exp\!\left({e}^{x} - 1\right)

Assumptions:

x \in \mathbb{C}

TeX:

\sum_{n=0}^{\infty} \frac{B_{n}}{n !} {x}^{n} = \exp\!\left({e}^{x} - 1\right)

x \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Sum`	$\sum_{n} f(n)$	Sum
`BellNumber`	$B_{n}$	Bell number
`Factorial`	$n !$	Factorial
`Pow`	${a}^{b}$	Power
`Infinity`	$\infty$	Positive infinity
`Exp`	${e}^{z}$	Exponential function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("aab4e3"),
    Formula(Equal(Sum(Mul(Div(BellNumber(n), Factorial(n)), Pow(x, n)), For(n, 0, Infinity)), Exp(Sub(Exp(x), 1)))),
    Variables(x),
    Assumptions(Element(x, CC)))

Topics using this entry

Bell numbers

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