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Fungrim entry: 8f5d76

RC ⁣(x,y)=2RC ⁣(x+λ,y+λ)   where λ=y+2xyR_C\!\left(x, y\right) = 2 R_C\!\left(x + \lambda, y + \lambda\right)\; \text{ where } \lambda = y + 2 \sqrt{x} \sqrt{y}
Assumptions:xC  and  yCx \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}
R_C\!\left(x, y\right) = 2 R_C\!\left(x + \lambda, y + \lambda\right)\; \text{ where } \lambda = y + 2 \sqrt{x} \sqrt{y}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(CarlsonRC(x, y), Where(Mul(2, CarlsonRC(Add(x, lamda), Add(y, lamda))), Def(lamda, Add(y, Mul(Mul(2, Sqrt(x)), Sqrt(y))))))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC))))

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2021-03-15 19:12:00.328586 UTC