# Fungrim entry: 21241f

$\left(x\right)_{n} = \sum_{k=0}^{n} \left[{n \atop k}\right] {x}^{k}$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}$
TeX:
\left(x\right)_{n} = \sum_{k=0}^{n} \left[{n \atop k}\right] {x}^{k}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
RisingFactorial$\left(z\right)_{k}$ Rising factorial
Sum$\sum_{n} f(n)$ Sum
StirlingCycle$\left[{n \atop k}\right]$ Unsigned Stirling number of the first kind
Pow${a}^{b}$ Power
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("21241f"),
Formula(Equal(RisingFactorial(x, n), Sum(Mul(StirlingCycle(n, k), Pow(x, k)), For(k, 0, n)))),
Variables(x, n),
Assumptions(And(Element(n, ZZGreaterEqual(0)), 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.

2021-03-15 19:12:00.328586 UTC