Fungrim entry: 18d955

\,{}_2F_1\!\left(a, b, c, 0\right) = 1

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \setminus \{0, -1, \ldots\}

TeX:

\,{}_2F_1\!\left(a, b, c, 0\right) = 1

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \setminus \{0, -1, \ldots\}

Definitions:

Fungrim symbol	Notation	Short description
`Hypergeometric2F1`	$\,{}_2F_1\!\left(a, b, c, z\right)$	Gauss hypergeometric 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("18d955"),
    Formula(Equal(Hypergeometric2F1(a, b, c, 0), 1)),
    Variables(a, b, c),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(c, SetMinus(CC, ZZLessEqual(0))))))

Topics using this entry

Gauss hypergeometric function

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