Fungrim entry: 97ba8d

{e}^{z + n \pi i} = {\left(-1\right)}^{n} {e}^{z}

Assumptions:

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}

TeX:

{e}^{z + n \pi i} = {\left(-1\right)}^{n} {e}^{z}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Exp`	${e}^{z}$	Exponential function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("97ba8d"),
    Formula(Equal(Exp(Add(z, Mul(Mul(n, Pi), ConstI))), Mul(Pow(-1, n), Exp(z)))),
    Variables(z, n),
    Assumptions(And(Element(z, CC), Element(n, ZZ))))

Topics using this entry

Exponential function

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