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

Carlson symmetric elliptic integrals