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Fungrim entry: 3141e4

B1 ⁣(a,b)=B ⁣(a,b)\mathrm{B}_{1}\!\left(a, b\right) = \mathrm{B}\!\left(a, b\right)
Assumptions:aC{0,1,}andbC{0,1,}a \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \{0, -1, \ldots\}
TeX:
\mathrm{B}_{1}\!\left(a, b\right) = \mathrm{B}\!\left(a, b\right)

a \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
IncompleteBetaBx ⁣(a,b)\mathrm{B}_{x}\!\left(a, b\right) Incomplete beta function
BetaFunctionB ⁣(a,b)\mathrm{B}\!\left(a, b\right) Beta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("3141e4"),
    Formula(Equal(IncompleteBeta(1, a, b), BetaFunction(a, b))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))))))

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

2019-11-11 15:50:15.016492 UTC