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Fungrim entry: bb4f41

B ⁣(m,n)=1m(m+n−1m)\mathrm{B}\!\left(m, n\right) = \frac{1}{m {m + n - 1 \choose m}}
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{1}{m {m + n - 1 \choose m}}

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
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("bb4f41"),
    Formula(Equal(BetaFunction(m, n), Div(1, Mul(m, Binomial(Sub(Add(m, n), 1), m))))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZGreaterEqual(1)), Element(n, ZZGreaterEqual(1)))))

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