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Fungrim entry: 223ce1

F2n+1=25T2n+1 ⁣(52)F_{2 n + 1} = \frac{2}{\sqrt{5}} T_{2 n + 1}\!\left(\frac{\sqrt{5}}{2}\right)
Assumptions:nZn \in \mathbb{Z}
TeX:
F_{2 n + 1} = \frac{2}{\sqrt{5}} T_{2 n + 1}\!\left(\frac{\sqrt{5}}{2}\right)

n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Sqrtz\sqrt{z} Principal square root
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("223ce1"),
    Formula(Equal(Fibonacci(Add(Mul(2, n), 1)), Mul(Div(2, Sqrt(5)), ChebyshevT(Add(Mul(2, n), 1), Div(Sqrt(5), 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.

2019-08-19 14:38:23.809000 UTC