Fungrim entry: 0ba9b2

\log(z) = \int_{1}^{z} \frac{1}{t} \, dt

Assumptions:

z \in \mathbb{C} \setminus \left(-\infty, 0\right]

TeX:

\log(z) = \int_{1}^{z} \frac{1}{t} \, dt

z \in \mathbb{C} \setminus \left(-\infty, 0\right]

Definitions:

Fungrim symbol	Notation	Short description
`Log`	$\log(z)$	Natural logarithm
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("0ba9b2"),
    Formula(Equal(Log(z), Integral(Div(1, t), For(t, 1, z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))))

Topics using this entry

Natural logarithm

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