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Fungrim entry: 741859

ddyRC ⁣(x,y)={12(xy)(RC ⁣(x,y)xy),xy13x3/2,x=y\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:xC(,0]  and  yC(,0]  and  xyx \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
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
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    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))))

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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