# Fungrim entry: c92da4

$I_{x}\!\left(a, b\right) = \frac{\mathrm{B}_{x}\!\left(a, b\right)}{\mathrm{B}\!\left(a, b\right)}$
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) = \frac{\mathrm{B}_{x}\!\left(a, b\right)}{\mathrm{B}\!\left(a, b\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
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("c92da4"),
Formula(Equal(IncompleteBetaRegularized(x, a, b), Div(IncompleteBeta(x, a, b), BetaFunction(a, b)))),
Variables(x, a, b),
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.

2020-03-29 16:01:42.585089 UTC