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Fungrim entry: 4d6416

ab=exp⁡ ⁣(blog⁡ ⁣(a)){a}^{b} = \exp\!\left(b \log\!\left(a\right)\right)
Assumptions:a∈C∖{0} and⁡ b∈Ca \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
TeX:
{a}^{b} = \exp\!\left(b \log\!\left(a\right)\right)

a \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
Expez{e}^{z} Exponential function
Loglog⁡ ⁣(z)\log\!\left(z\right) Natural logarithm
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("4d6416"),
    Formula(Equal(Pow(a, b), Exp(Mul(b, Log(a))))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(CC, Set(0))), Element(b, CC))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC