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# Fungrim entry: e1a3cb

$R_J\!\left(0, 0, z, w\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{z} w}\right) \infty, & z \ne 0 \;\mathbin{\operatorname{and}}\; w \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C}$
TeX:
R_J\!\left(0, 0, z, w\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{z} w}\right) \infty, & z \ne 0 \;\mathbin{\operatorname{and}}\; w \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \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
Sign$\operatorname{sgn}(z)$ Sign function
Sqrt$\sqrt{z}$ Principal square root
Infinity$\infty$ Positive infinity
UnsignedInfinity${\tilde \infty}$ Unsigned infinity
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("e1a3cb"),
Formula(Equal(CarlsonRJ(0, 0, z, w), Cases(Tuple(Mul(Sign(Div(1, Mul(Sqrt(z), w))), Infinity), And(NotEqual(z, 0), NotEqual(w, 0))), Tuple(UnsignedInfinity, Otherwise)))),
Variables(z, w),
Assumptions(And(Element(z, CC), Element(w, 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