Fungrim entry: fe6e74

\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) = \frac{\,{}_2F_1\!\left(a, b, c, z\right)}{\Gamma\!\left(c\right)}

Assumptions:

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}

TeX:

\,{}_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}

Definitions:

Fungrim symbol	Notation	Short description
`Hypergeometric2F1Regularized`	$\,{}_2{\textbf F}_1\!\left(a, b, c, z\right)$	Regularized Gauss hypergeometric function
`Hypergeometric2F1`	$\,{}_2F_1\!\left(a, b, c, z\right)$	Gauss hypergeometric function
`GammaFunction`	$\Gamma\!\left(z\right)$	Gamma function
`CC`	$\mathbb{C}$	Complex numbers
`ZZLessEqual`	$\mathbb{Z}_{\le n}$	Integers less than or equal to n

Source code for this entry:

Entry(ID("fe6e74"),
    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))))

Topics using this entry

Gauss hypergeometric function