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Fungrim entry: 7cddc6

RG ⁣(0,x,y)=xE ⁣(1yx)2R_G\!\left(0, x, y\right) = \frac{\sqrt{x} E\!\left(1 - \frac{y}{x}\right)}{2}
Assumptions:xC  and  yC  and  arg(x)arg(y)<πx \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(x) - \arg(y)\right| < \pi
R_G\!\left(0, x, y\right) = \frac{\sqrt{x} E\!\left(1 - \frac{y}{x}\right)}{2}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(x) - \arg(y)\right| < \pi
Fungrim symbol Notation Short description
CarlsonRGRG ⁣(x,y,z)R_G\!\left(x, y, z\right) Carlson symmetric elliptic integral of the second kind
Sqrtz\sqrt{z} Principal square root
EllipticEE(m)E(m) Legendre complete elliptic integral of the second kind
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Argarg(z)\arg(z) Complex argument
Piπ\pi The constant pi (3.14...)
Source code for this entry:
    Formula(Equal(CarlsonRG(0, x, y), Div(Mul(Sqrt(x), EllipticE(Sub(1, Div(y, x)))), 2))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC), Less(Abs(Sub(Arg(x), Arg(y))), Pi))))

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2021-03-15 19:12:00.328586 UTC