Fungrim entry: f9f31d

\sqrt{{e}^{i \theta} \infty} = {e}^{i \theta / 2} \infty

Assumptions:

\theta \in \left(-\pi, \pi\right]

TeX:

\sqrt{{e}^{i \theta} \infty} = {e}^{i \theta / 2} \infty

\theta \in \left(-\pi, \pi\right]

Definitions:

Fungrim symbol	Notation	Short description
`Sqrt`	$\sqrt{z}$	Principal square root
`Exp`	${e}^{z}$	Exponential function
`ConstI`	$i$	Imaginary unit
`Infinity`	$\infty$	Positive infinity
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Pi`	$\pi$	The constant pi (3.14...)

Source code for this entry:

Entry(ID("f9f31d"),
    Formula(Equal(Sqrt(Mul(Exp(Mul(ConstI, theta)), Infinity)), Mul(Exp(Div(Mul(ConstI, theta), 2)), Infinity))),
    Variables(theta),
    Assumptions(Element(theta, OpenClosedInterval(Neg(Pi), Pi))))

Topics using this entry

Square roots

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