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Fungrim entry: 90c290

Fn= 2F1 ⁣(1−n2,2−n2,1−n,−4)F_{n} = \,{}_2F_1\!\left(\frac{1 - n}{2}, \frac{2 - n}{2}, 1 - n, -4\right)
Assumptions:n∈Z≥1n \in \mathbb{Z}_{\ge 1}
TeX:
F_{n} = \,{}_2F_1\!\left(\frac{1 - n}{2}, \frac{2 - n}{2}, 1 - n, -4\right)

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
Hypergeometric2F1 2F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("90c290"),
    Formula(Equal(Fibonacci(n), Hypergeometric2F1(Div(Sub(1, n), 2), Div(Sub(2, n), 2), Sub(1, n), -4))),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(1))))

Topics using this entry

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