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Fungrim entry: ae76a3

Fn=in−1Un−1 ⁣(−i2)F_{n} = {i}^{n - 1} U_{n - 1}\!\left(-\frac{i}{2}\right)
Assumptions:n∈Zn \in \mathbb{Z}
TeX:
F_{n} = {i}^{n - 1} U_{n - 1}\!\left(-\frac{i}{2}\right)

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
ConstIii Imaginary unit
ChebyshevUUn ⁣(x)U_{n}\!\left(x\right) Chebyshev polynomial of the second kind
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("ae76a3"),
    Formula(Equal(Fibonacci(n), Mul(Pow(ConstI, Sub(n, 1)), ChebyshevU(Sub(n, 1), Neg(Div(ConstI, 2)))))),
    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.

2021-03-15 19:12:00.328586 UTC