Fungrim home page

Fungrim entry: 31a3ba

RD ⁣(x,y,z)=2RD ⁣(x+λ,y+λ,z+λ)+3z(z+λ)   where λ=xy+yz+xzR_D\!\left(x, y, z\right) = 2 R_D\!\left(x + \lambda, y + \lambda, z + \lambda\right) + \frac{3}{\sqrt{z} \left(z + \lambda\right)}\; \text{ where } \lambda = \sqrt{x} \sqrt{y} + \sqrt{y} \sqrt{z} + \sqrt{x} \sqrt{z}
Assumptions:xC  and  yC  and  zC  and  z0x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
R_D\!\left(x, y, z\right) = 2 R_D\!\left(x + \lambda, y + \lambda, z + \lambda\right) + \frac{3}{\sqrt{z} \left(z + \lambda\right)}\; \text{ where } \lambda = \sqrt{x} \sqrt{y} + \sqrt{y} \sqrt{z} + \sqrt{x} \sqrt{z}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
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
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(CarlsonRD(x, y, z), Where(Add(Mul(2, CarlsonRD(Add(x, lamda), Add(y, lamda), Add(z, lamda))), Div(3, Mul(Sqrt(z), Add(z, lamda)))), Def(lamda, Add(Add(Mul(Sqrt(x), Sqrt(y)), Mul(Sqrt(y), Sqrt(z))), Mul(Sqrt(x), Sqrt(z))))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), NotEqual(z, 0))))

Topics using this entry

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