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Fungrim entry: fe6e74

2F1 ⁣(a,b,c,z)=2F1 ⁣(a,b,c,z)Γ ⁣(c)\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) = \frac{\,{}_2F_1\!\left(a, b, c, z\right)}{\Gamma\!\left(c\right)}
Assumptions:aCandbCandcC{0,1,}andzCa \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) = \frac{\,{}_2F_1\!\left(a, b, c, z\right)}{\Gamma\!\left(c\right)}

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Fungrim symbol Notation Short description
Hypergeometric2F1Regularized2F1 ⁣(a,b,c,z)\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) Regularized Gauss hypergeometric function
Hypergeometric2F12F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
    Formula(Equal(Hypergeometric2F1Regularized(a, b, c, z), Div(Hypergeometric2F1(a, b, c, z), GammaFunction(c)))),
    Variables(a, b, c, z),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(c, SetMinus(CC, ZZLessEqual(0))), Element(z, CC))))

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

2019-09-15 11:00:55.020619 UTC