# Fungrim entry: 771801

$R_D\!\left(x, x, y\right) = \begin{cases} \frac{3}{y - x} \left(R_C\!\left(y, x\right) - \frac{1}{\sqrt{y}}\right), & x \ne y\\{x}^{-3 / 2}, & x = y\\ \end{cases}$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}$
TeX:
R_D\!\left(x, x, y\right) = \begin{cases} \frac{3}{y - x} \left(R_C\!\left(y, x\right) - \frac{1}{\sqrt{y}}\right), & x \ne y\\{x}^{-3 / 2}, & x = y\\ \end{cases}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRD$R_D\!\left(x, y, z\right)$ Degenerate Carlson symmetric elliptic integral of the third kind
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first kind
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("771801"),
Formula(Equal(CarlsonRD(x, x, y), Cases(Tuple(Mul(Div(3, Sub(y, x)), Sub(CarlsonRC(y, x), Div(1, Sqrt(y)))), NotEqual(x, y)), Tuple(Pow(x, Neg(Div(3, 2))), Equal(x, y))))),
Variables(x, y),
Assumptions(And(Element(x, CC), 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