Fungrim entry: d651d1

$\left(z\right)_{2 k} = {4}^{k} \left(\frac{z}{2}\right)_{k} \left(\frac{z + 1}{2}\right)_{k}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$
TeX:
\left(z\right)_{2 k} = {4}^{k} \left(\frac{z}{2}\right)_{k} \left(\frac{z + 1}{2}\right)_{k}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
RisingFactorial$\left(z\right)_{k}$ Rising factorial
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("d651d1"),
Formula(Equal(RisingFactorial(z, Mul(2, k)), Mul(Mul(Pow(4, k), RisingFactorial(Div(z, 2), k)), RisingFactorial(Div(Add(z, 1), 2), k)))),
Variables(z, k),
Assumptions(And(Element(z, CC), Element(k, ZZGreaterEqual(0)))))

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