Fungrim entry: 3141e4

\mathrm{B}_{1}\!\left(a, b\right) = \mathrm{B}\!\left(a, b\right)

Assumptions:

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
`IncompleteBeta`	$\mathrm{B}_{x}\!\left(a, b\right)$	Incomplete beta function
`BetaFunction`	$\mathrm{B}\!\left(a, b\right)$	Beta function
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	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))))))

Topics using this entry

Beta function

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