Fungrim entry: 19f13b

\left(z\right)_{k} = \prod_{i=1}^{k} \left(z + i - 1\right) = \prod_{i=0}^{k - 1} \left(z + i\right)

Assumptions:

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, k \in \mathbb{Z}_{\ge 0}

TeX:

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
`CC`	$\mathbb{C}$	Complex numbers
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n

Source code for this entry:

Entry(ID("19f13b"),
    Equal(RisingFactorial(z, k), Product(Parentheses(Sub(Add(z, i), 1)), Tuple(i, 1, k)), Product(Parentheses(Add(z, i)), Tuple(i, 0, Sub(k, 1)))),
    Variables(z, k),
    Assumptions(And(Element(z, CC), Element(k, ZZGreaterEqual(0)))))

Topics using this entry

Factorials and binomial coefficients

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

2019-06-18 07:49:59.356594 UTC