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Fungrim entry: b25089

2F1 ⁣(a,b,c,z)=(1z)a2F1 ⁣(a,cb,c,zz1)\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) = {\left(1 - z\right)}^{-a} \,{}_2{\textbf F}_1\!\left(a, c - b, c, \frac{z}{z - 1}\right)
Assumptions:aCandbCandcCandzCandz1a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \ne 1
TeX:
\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) = {\left(1 - z\right)}^{-a} \,{}_2{\textbf F}_1\!\left(a, c - b, c, \frac{z}{z - 1}\right)

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \ne 1
Definitions:
Fungrim symbol Notation Short description
Hypergeometric2F1Regularized2F1 ⁣(a,b,c,z)\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) Regularized Gauss hypergeometric function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("b25089"),
    Formula(Equal(Hypergeometric2F1Regularized(a, b, c, z), Mul(Pow(Sub(1, z), Neg(a)), Hypergeometric2F1Regularized(a, Sub(c, b), c, Div(z, Sub(z, 1)))))),
    Variables(a, b, c, z),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(c, CC), Element(z, CC), Unequal(z, 1))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC