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Fungrim entry: aadf90

F2n=Un−1 ⁣(32)F_{2 n} = U_{n - 1}\!\left(\frac{3}{2}\right)
Assumptions:n∈Zn \in \mathbb{Z}
TeX:
F_{2 n} = U_{n - 1}\!\left(\frac{3}{2}\right)

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
ChebyshevUUn ⁣(x)U_{n}\!\left(x\right) Chebyshev polynomial of the second kind
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("aadf90"),
    Formula(Equal(Fibonacci(Mul(2, n)), ChebyshevU(Sub(n, 1), Div(3, 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