# Fungrim entry: f3b8dc

$R_C\!\left(x, y\right) = \frac{1}{2} \int_{0}^{\infty} \frac{1}{\left(t + y\right) \sqrt{t + x}} \, dt$
Assumptions:$x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]$
TeX:
R_C\!\left(x, y\right) = \frac{1}{2} \int_{0}^{\infty} \frac{1}{\left(t + y\right) \sqrt{t + x}} \, dt

x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]
Definitions:
Fungrim symbol Notation Short description
CarlsonRC$R_C\!\left(x, y\right)$ Degenerate Carlson symmetric elliptic integral of the first kind
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Sqrt$\sqrt{z}$ Principal square root
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
OpenInterval$\left(a, b\right)$ Open interval
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Source code for this entry:
Entry(ID("f3b8dc"),
Formula(Equal(CarlsonRC(x, y), Mul(Div(1, 2), Integral(Div(1, Mul(Add(t, y), Sqrt(Add(t, x)))), For(t, 0, Infinity))))),
Variables(x, y),
Assumptions(And(Element(x, SetMinus(CC, OpenInterval(Neg(Infinity), 0))), Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))

## 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