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Fungrim entry: 24107d

Fn=φn(φ)n5F_{n} = \frac{{\varphi}^{n} - {\left(-\varphi\right)}^{-n}}{\sqrt{5}}
Assumptions:nZn \in \mathbb{Z}
TeX:
F_{n} = \frac{{\varphi}^{n} - {\left(-\varphi\right)}^{-n}}{\sqrt{5}}

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
GoldenRatioφ\varphi The golden ratio (1.618...)
Sqrtz\sqrt{z} Principal square root
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("24107d"),
    Formula(Equal(Fibonacci(n), Div(Sub(Pow(GoldenRatio, n), Pow(Neg(GoldenRatio), Neg(n))), Sqrt(5)))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

Topics using this entry

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