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Fungrim entry: 415ff0

RF ⁣(0,x,y)=K ⁣(1yx)xR_F\!\left(0, x, y\right) = \frac{K\!\left(1 - \frac{y}{x}\right)}{\sqrt{x}}
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_F\!\left(0, x, y\right) = \frac{K\!\left(1 - \frac{y}{x}\right)}{\sqrt{x}}

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
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first kind
EllipticKK(m)K(m) Legendre complete elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
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(CarlsonRF(0, x, y), Div(EllipticK(Sub(1, Div(y, x))), Sqrt(x)))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC), Less(Abs(Sub(Arg(x), Arg(y))), Pi))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC