# Fungrim entry: a7dbf6

$\mathrm{B}\!\left(-n, b\right) = \begin{cases} \frac{{\left(-1\right)}^{b}}{b {n \choose b}}, & b \in \{1, 2, \ldots, n\}\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}$
TeX:
\mathrm{B}\!\left(-n, b\right) = \begin{cases} \frac{{\left(-1\right)}^{b}}{b {n \choose b}}, & b \in \{1, 2, \ldots, n\}\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BetaFunction$\mathrm{B}\!\left(a, b\right)$ Beta function
Pow${a}^{b}$ Power
Binomial${n \choose k}$ Binomial coefficient
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
UnsignedInfinity${\tilde \infty}$ Unsigned infinity
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("a7dbf6"),
Formula(Equal(BetaFunction(Neg(n), b), Cases(Tuple(Div(Pow(-1, b), Mul(b, Binomial(n, b))), Element(b, Range(1, n))), Tuple(UnsignedInfinity, Otherwise)))),
Variables(n, b),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(b, CC))))

## Topics using this entry

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

2020-03-29 16:01:42.585089 UTC