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Fungrim entry: 157ebb

RC ⁣(1,1+y)= 2F1 ⁣(1,12,32,−y)R_C\!\left(1, 1 + y\right) = \,{}_2F_1\!\left(1, \frac{1}{2}, \frac{3}{2}, -y\right)
Assumptions:y∈Cy \in \mathbb{C}
TeX:
R_C\!\left(1, 1 + y\right) = \,{}_2F_1\!\left(1, \frac{1}{2}, \frac{3}{2}, -y\right)

y \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Hypergeometric2F1 2F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("157ebb"),
    Formula(Equal(CarlsonRC(1, Add(1, y)), Hypergeometric2F1(1, Div(1, 2), Div(3, 2), Neg(y)))),
    Variables(y),
    Assumptions(Element(y, CC)))

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2021-03-15 19:12:00.328586 UTC