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# Fungrim entry: 72db94

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

n \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BetaFunction$\mathrm{B}\!\left(a, b\right)$ Beta function
UnsignedInfinity${\tilde \infty}$ Unsigned infinity
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
Binomial${n \choose k}$ Binomial coefficient
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("72db94"),
Formula(Equal(BetaFunction(n, b), Cases(Tuple(UnsignedInfinity, Element(Neg(b), Range(0, Sub(n, 1)))), Tuple(Div(1, Mul(n, Binomial(Sub(Add(n, b), 1), n))), Otherwise)))),
Variables(n, b),
Assumptions(And(Element(n, ZZGreaterEqual(1)), 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.

2021-03-15 19:12:00.328586 UTC