# Fungrim entry: 315b3d

$I_{x}\!\left(a, b\right) = 1 - I_{1 - x}\!\left(b, a\right)$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; a + b \notin \{0, -1, \ldots\}$
TeX:
I_{x}\!\left(a, b\right) = 1 - I_{1 - x}\!\left(b, a\right)

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; a + b \notin \{0, -1, \ldots\}
Definitions:
Fungrim symbol Notation Short description
IncompleteBetaRegularized$I_{x}\!\left(a, b\right)$ Regularized incomplete 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("315b3d"),
Formula(Equal(IncompleteBetaRegularized(x, a, b), Sub(1, IncompleteBetaRegularized(Sub(1, x), b, a)))),
Variables(a, b, x),
Assumptions(And(Element(x, CC), Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))), NotElement(Add(a, b), 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