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Fungrim entry: 6c2b31

zn+1=znz{z}^{n + 1} = {z}^{n} z
Assumptions:z∈C  and⁡  n∈Z≥0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Alternative assumptions:z∈R  and⁡  R∈Rings⁡  and⁡  n∈Z≥0z \in R \;\mathbin{\operatorname{and}}\; R \in \operatorname{Rings} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
TeX:
{z}^{n + 1} = {z}^{n} z

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}

z \in R \;\mathbin{\operatorname{and}}\; R \in \operatorname{Rings} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("6c2b31"),
    Formula(Mul(Equal(Pow(z, Add(n, 1)), Pow(z, n)), z)),
    Variables(z, n),
    Assumptions(And(Element(z, CC), Element(n, ZZGreaterEqual(0))), And(Element(z, R), Element(R, Rings), Element(n, ZZGreaterEqual(0)))))

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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