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Fungrim entry: a2e9dd

RG ⁣(0,x,cx)=xE ⁣(1c)2R_G\!\left(0, x, c x\right) = \frac{\sqrt{x} E\!\left(1 - c\right)}{2}
Assumptions:xC  and  c[0,)x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)
R_G\!\left(0, x, c x\right) = \frac{\sqrt{x} E\!\left(1 - c\right)}{2}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)
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
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(CarlsonRG(0, x, Mul(c, x)), Div(Mul(Sqrt(x), EllipticE(Sub(1, c))), 2))),
    Variables(x, c),
    Assumptions(And(Element(x, CC), Element(c, ClosedOpenInterval(0, Infinity)))))

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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