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Fungrim entry: 315b3d

Ix ⁣(a,b)=1I1x ⁣(b,a)I_{x}\!\left(a, b\right) = 1 - I_{1 - x}\!\left(b, a\right)
Assumptions:xCandaC{0,1,}andbC{0,1,}anda+b{0,1,}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
IncompleteBetaRegularizedIx ⁣(a,b)I_{x}\!\left(a, b\right) Regularized incomplete beta function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\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),
    Assumptions(And(Element(x, CC), Element(a, SetMinus(CC, ZZLessEqual(0))), Element(b, SetMinus(CC, ZZLessEqual(0))), NotElement(Add(a, b), ZZLessEqual(0)))))

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2019-10-05 13:11:19.856591 UTC