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Fungrim entry: 3e71f4

d2dz2z=−14z3/2\frac{d^{2}}{{d z}^{2}} \sqrt{z} = -\frac{1}{4 {z}^{3 / 2}}
Assumptions:z∈C∖(−∞,0]z \in \mathbb{C} \setminus \left(-\infty, 0\right]
TeX:
\frac{d^{2}}{{d z}^{2}} \sqrt{z} = -\frac{1}{4 {z}^{3 / 2}}

z \in \mathbb{C} \setminus \left(-\infty, 0\right]
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddz f ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
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:
Entry(ID("3e71f4"),
    Formula(Equal(ComplexDerivative(Sqrt(z), For(z, z, 2)), Neg(Div(1, Mul(4, Pow(z, Div(3, 2))))))),
    Variables(z),
    Assumptions(Element(z, 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