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Fungrim entry: 4d6416

ab=eblog⁡(a){a}^{b} = {e}^{b \log(a)}
Assumptions:a∈C∖{0}  and⁡  b∈Ca \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
TeX:
{a}^{b} = {e}^{b \log(a)}

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(z) 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

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2021-03-15 19:12:00.328586 UTC