Assumptions:
TeX:
\,{}_2{\textbf F}_1\!\left(a, b, c, z\right) = \frac{\,{}_2F_1\!\left(a, b, c, z\right)}{\Gamma(c)} 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 | Regularized Gauss hypergeometric function | |
Hypergeometric2F1 | Gauss hypergeometric function | |
Gamma | Gamma function | |
CC | Complex numbers | |
ZZLessEqual | 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), Gamma(c)))), Variables(a, b, c, z), Assumptions(And(Element(a, CC), Element(b, CC), Element(c, SetMinus(CC, ZZLessEqual(0))), Element(z, CC))))