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

Gauss hypergeometric function