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Fungrim entry: 082a69

B ⁣(m,n)=(m−1)!(n−1)!(m+n−1)!\mathrm{B}\!\left(m, n\right) = \frac{\left(m - 1\right)! \left(n - 1\right)!}{\left(m + n - 1\right)!}
Assumptions:m∈Z≥1  and⁡  n∈Z≥1m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
TeX:
\mathrm{B}\!\left(m, n\right) = \frac{\left(m - 1\right)! \left(n - 1\right)!}{\left(m + n - 1\right)!}

m \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
BetaFunctionB ⁣(a,b)\mathrm{B}\!\left(a, b\right) Beta function
Factorialn!n ! Factorial
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("082a69"),
    Formula(Equal(BetaFunction(m, n), Div(Mul(Factorial(Sub(m, 1)), Factorial(Sub(n, 1))), Factorial(Sub(Add(m, n), 1))))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(n, ZZGreaterEqual(1)))))

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2021-03-15 19:12:00.328586 UTC