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Fungrim entry: c4d78a

Fn=25(−i)nsinh⁡ ⁣(n(log⁡(φ)+12πi))F_{n} = \frac{2}{\sqrt{5}} {\left(-i\right)}^{n} \sinh\!\left(n \left(\log(\varphi) + \frac{1}{2} \pi i\right)\right)
Assumptions:n∈Zn \in \mathbb{Z}
TeX:
F_{n} = \frac{2}{\sqrt{5}} {\left(-i\right)}^{n} \sinh\!\left(n \left(\log(\varphi) + \frac{1}{2} \pi i\right)\right)

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
ConstIii Imaginary unit
Loglog⁡(z)\log(z) Natural logarithm
GoldenRatioφ\varphi The golden ratio (1.618...)
Piπ\pi The constant pi (3.14...)
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("c4d78a"),
    Formula(Equal(Fibonacci(n), Mul(Mul(Div(2, Sqrt(5)), Pow(Neg(ConstI), n)), Sinh(Mul(n, Add(Log(GoldenRatio), Mul(Mul(Div(1, 2), Pi), ConstI))))))),
    Variables(n),
    Assumptions(Element(n, ZZ)))

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2021-03-15 19:12:00.328586 UTC