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Fungrim entry: 538c8c

RF ⁣(0,x,cx)=K ⁣(1c)xR_F\!\left(0, x, c x\right) = \frac{K\!\left(1 - c\right)}{\sqrt{x}}
Assumptions:xC  and  c[0,)x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)
R_F\!\left(0, x, c x\right) = \frac{K\!\left(1 - c\right)}{\sqrt{x}}

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