# Fungrim entry: eb1d4f

$R_C\!\left(1, 1 + y\right) = \begin{cases} \frac{\operatorname{atan}\!\left(\sqrt{y}\right)}{\sqrt{y}}, & y \ne 0\\1, & y = 0\\ \end{cases}$
Assumptions:$y \in \mathbb{C}$
TeX:
R_C\!\left(1, 1 + y\right) = \begin{cases} \frac{\operatorname{atan}\!\left(\sqrt{y}\right)}{\sqrt{y}}, & y \ne 0\\1, & y = 0\\ \end{cases}

y \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first kind
Atan$\operatorname{atan}(z)$ Inverse tangent
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("eb1d4f"),
Formula(Equal(CarlsonRC(1, Add(1, y)), Cases(Tuple(Div(Atan(Sqrt(y)), Sqrt(y)), NotEqual(y, 0)), Tuple(1, Equal(y, 0))))),
Variables(y),
Assumptions(Element(y, 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