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Fungrim entry: a203e9

RD ⁣(λ,x+λ,y+λ)+RD ⁣(μ,x+μ,y+μ)=RD ⁣(0,x,y)3yx+y+λ+μ   where μ=xyλR_D\!\left(\lambda, x + \lambda, y + \lambda\right) + R_D\!\left(\mu, x + \mu, y + \mu\right) = R_D\!\left(0, x, y\right) - \frac{3}{y \sqrt{x + y + \lambda + \mu}}\; \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_D\!\left(\lambda, x + \lambda, y + \lambda\right) + R_D\!\left(\mu, x + \mu, y + \mu\right) = R_D\!\left(0, x, y\right) - \frac{3}{y \sqrt{x + y + \lambda + \mu}}\; \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
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
Sqrtz\sqrt{z} Principal square root
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(CarlsonRD(lamda, Add(x, lamda), Add(y, lamda)), CarlsonRD(mu, Add(x, mu), Add(y, mu))), Sub(CarlsonRD(0, x, y), Div(3, Mul(y, Sqrt(Add(Add(Add(x, y), lamda), mu)))))), 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