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Fungrim entry: 3b6175

$R_J\!\left(0, y, z, \sqrt{y} \sqrt{z}\right) = \frac{3}{2 \sqrt{y} \sqrt{z}} R_F\!\left(0, y, z\right)$
Assumptions:$y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}$
TeX:
R_J\!\left(0, y, z, \sqrt{y} \sqrt{z}\right) = \frac{3}{2 \sqrt{y} \sqrt{z}} R_F\!\left(0, y, z\right)

y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRJ$R_J\!\left(x, y, z, w\right)$ Carlson symmetric elliptic integral of the third kind
Sqrt$\sqrt{z}$ Principal square root
CarlsonRF$R_F\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the first kind
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("3b6175"),
Formula(Equal(CarlsonRJ(0, y, z, Mul(Sqrt(y), Sqrt(z))), Mul(Div(3, Mul(2, Mul(Sqrt(y), Sqrt(z)))), CarlsonRF(0, y, z)))),
Variables(y, z),
Assumptions(And(Element(y, CC), Element(z, CC))))

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