Fungrim entry: ff613a

$I_{0}\!\left(a, b\right) = 0$
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_{0}\!\left(a, b\right) = 0

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("ff613a"),
Formula(Equal(IncompleteBetaRegularized(0, a, b), 0)),
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