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# Fungrim entry: 20bf69

$\,{}_2F_1\!\left(a, b, b, z\right) = {\left(1 - z\right)}^{-a}$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0, 1\right\}$
TeX:
\,{}_2F_1\!\left(a, b, b, z\right) = {\left(1 - z\right)}^{-a}

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \{0, -1, \ldots\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0, 1\right\}
Definitions:
Fungrim symbol Notation Short description
Hypergeometric2F1$\,{}_2F_1\!\left(a, b, c, z\right)$ Gauss hypergeometric function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ZZLessEqual$\mathbb{Z}_{\le n}$ Integers less than or equal to n
Source code for this entry:
Entry(ID("20bf69"),
Formula(Equal(Hypergeometric2F1(a, b, b, z), Pow(Sub(1, z), Neg(a)))),
Variables(a, b, z),
Assumptions(And(Element(a, CC), Element(b, SetMinus(CC, ZZLessEqual(0))), Element(z, SetMinus(CC, Set(0, 1))))))

## Topics using this entry

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2021-03-15 19:12:00.328586 UTC