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Fungrim entry: f3b8dc

RC ⁣(x,y)=1201(t+y)t+xdtR_C\!\left(x, y\right) = \frac{1}{2} \int_{0}^{\infty} \frac{1}{\left(t + y\right) \sqrt{t + x}} \, dt
Assumptions:xC(,0)  and  yC(,0]x \in \mathbb{C} \setminus \left(-\infty, 0\right) \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right]
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]
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Integralabf(x)dx\int_{a}^{b} f(x) \, dx Integral
Sqrtz\sqrt{z} Principal square root
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
OpenInterval(a,b)\left(a, b\right) Open interval
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Source code for this entry:
    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))))))

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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