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Fungrim entry: aab4e3

n=0Bnn!xn=exp ⁣(ex1)\sum_{n=0}^{\infty} \frac{B_{n}}{n !} {x}^{n} = \exp\!\left({e}^{x} - 1\right)
Assumptions:xCx \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
Sumnf(n)\sum_{n} f(n) Sum
BellNumberBnB_{n} Bell number
Factorialn!n ! Factorial
Powab{a}^{b} Power
Infinity\infty Positive infinity
Expez{e}^{z} Exponential function
CCC\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

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

2020-08-27 09:56:25.682319 UTC