Fungrim home page

# Fungrim entry: 3e71f4

$\frac{d^{2}}{{d z}^{2}} \sqrt{z} = -\frac{1}{4 {z}^{3 / 2}}$
Assumptions:$z \in \mathbb{C} \setminus \left(-\infty, 0\right]$
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
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
OpenClosedInterval$\left(a, b\right]$ 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.

2020-01-31 18:09:28.494564 UTC