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Fungrim entry: 6a11ce

φn=Fnφ+Fn1{\varphi}^{n} = F_{n} \varphi + F_{n - 1}
Assumptions:nZn \in \mathbb{Z}
TeX:
{\varphi}^{n} = F_{n} \varphi + F_{n - 1}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
GoldenRatioφ\varphi The golden ratio (1.618...)
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("6a11ce"),
    Formula(Equal(Pow(GoldenRatio, n), Add(Mul(Fibonacci(n), GoldenRatio), Fibonacci(Sub(n, 1))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

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

2019-10-05 13:11:19.856591 UTC