Fungrim entry: 6a11ce

{\varphi}^{n} = F_{n} \varphi + F_{n - 1}

Assumptions:

n \in \mathbb{Z}

TeX:

{\varphi}^{n} = F_{n} \varphi + F_{n - 1}

n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`GoldenRatio`	$\varphi$	The golden ratio (1.618...)
`Fibonacci`	$F_{n}$	Fibonacci number
`ZZ`	$\mathbb{Z}$	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)))

Topics using this entry

Golden ratio

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