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Fungrim entry: 20bf69

2F1 ⁣(a,b,b,z)=(1z)a\,{}_2F_1\!\left(a, b, b, z\right) = {\left(1 - z\right)}^{-a}
Assumptions:aC  and  bC{0,1,}  and  zC{0,1}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\}
\,{}_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\}
Fungrim symbol Notation Short description
Hypergeometric2F12F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    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))))))

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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