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Fungrim entry: 8e6189

RF ⁣(x,y,z)=RF ⁣(x+λ4,y+λ4,z+λ4)   where λ=xy+yz+xzR_F\!\left(x, y, z\right) = R_F\!\left(\frac{x + \lambda}{4}, \frac{y + \lambda}{4}, \frac{z + \lambda}{4}\right)\; \text{ where } \lambda = \sqrt{x} \sqrt{y} + \sqrt{y} \sqrt{z} + \sqrt{x} \sqrt{z}
Assumptions:xC  and  yC  and  zCx \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
R_F\!\left(x, y, z\right) = R_F\!\left(\frac{x + \lambda}{4}, \frac{y + \lambda}{4}, \frac{z + \lambda}{4}\right)\; \text{ where } \lambda = \sqrt{x} \sqrt{y} + \sqrt{y} \sqrt{z} + \sqrt{x} \sqrt{z}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Fungrim symbol Notation Short description
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) 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(CarlsonRF(x, y, z), Where(CarlsonRF(Div(Add(x, lamda), 4), Div(Add(y, lamda), 4), Div(Add(z, lamda), 4)), Def(lamda, Add(Add(Mul(Sqrt(x), Sqrt(y)), Mul(Sqrt(y), Sqrt(z))), Mul(Sqrt(x), Sqrt(z))))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC))))

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2021-03-15 19:12:00.328586 UTC