# Fungrim entry: 741859

$\frac{d}{d y}\, R_C\!\left(x, y\right) = \begin{cases} \frac{1}{2 \left(x - y\right)} \left(R_C\!\left(x, y\right) - \frac{\sqrt{x}}{y}\right), & x \ne y\\-\frac{1}{3} {x}^{-3 / 2}, & x = y\\ \end{cases}$
Assumptions:$x \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; x \ne y$
TeX:
x \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; x \ne y
Definitions:
Fungrim symbol Notation Short description
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
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
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("741859"),
Equal(ComplexDerivative(CarlsonRC(x, y), For(y, y)), Cases(Tuple(Mul(Div(1, Mul(2, Sub(x, y))), Sub(CarlsonRC(x, y), Div(Sqrt(x), y))), NotEqual(x, y)), Tuple(Neg(Mul(Div(1, 3), Pow(x, Neg(Div(3, 2))))), Equal(x, y)))),
Variables(x, y),
Assumptions(And(Element(x, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), NotEqual(x, y))))

## 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