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Fungrim entry: 38fa65

RF ⁣(x+λ,y+λ,λ)+RF ⁣(x+μ,y+μ,μ)=RF ⁣(x,y,0)   where μ=xyλR_F\!\left(x + \lambda, y + \lambda, \lambda\right) + R_F\!\left(x + \mu, y + \mu, \mu\right) = R_F\!\left(x, y, 0\right)\; \text{ where } \mu = \frac{x y}{\lambda}
Assumptions:x(0,)  and  y(0,)  and  λC(,0]x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; \lambda \in \mathbb{C} \setminus \left(-\infty, 0\right]
R_F\!\left(x + \lambda, y + \lambda, \lambda\right) + R_F\!\left(x + \mu, y + \mu, \mu\right) = R_F\!\left(x, y, 0\right)\; \text{ where } \mu = \frac{x y}{\lambda}

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; \lambda \in \mathbb{C} \setminus \left(-\infty, 0\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
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Source code for this entry:
    Formula(Where(Equal(Add(CarlsonRF(Add(x, lamda), Add(y, lamda), lamda), CarlsonRF(Add(x, mu), Add(y, mu), mu)), CarlsonRF(x, y, 0)), Def(mu, Div(Mul(x, y), lamda)))),
    Variables(x, y, lamda),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)), Element(lamda, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))

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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