# 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

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