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Fungrim entry: 6dda7a

RD ⁣(x,y,z)+RD ⁣(y,z,x)+RD ⁣(z,x,y)=3xyzR_D\!\left(x, y, z\right) + R_D\!\left(y, z, x\right) + R_D\!\left(z, x, y\right) = \frac{3}{\sqrt{x} \sqrt{y} \sqrt{z}}
Assumptions:xC  and  yC  and  zC  and  x0  and  y0x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0
Alternative assumptions:z0z \ne 0
R_D\!\left(x, y, z\right) + R_D\!\left(y, z, x\right) + R_D\!\left(z, x, y\right) = \frac{3}{\sqrt{x} \sqrt{y} \sqrt{z}}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0

z \ne 0
Fungrim symbol Notation Short description
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Add(Add(CarlsonRD(x, y, z), CarlsonRD(y, z, x)), CarlsonRD(z, x, y)), Div(3, Mul(Mul(Sqrt(x), Sqrt(y)), Sqrt(z))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), NotEqual(x, 0), NotEqual(y, 0)), NotEqual(z, 0)))

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2021-03-15 19:12:00.328586 UTC