Fungrim entry: 1c90fb

F_{n} = \frac{n}{{2}^{n - 1}} \,{}_2F_1\!\left(\frac{1 - n}{2}, \frac{2 - n}{2}, \frac{3}{2}, 5\right)

Assumptions:

n \in \mathbb{Z}

References:

http://functions.wolfram.com/IntegerFunctions/Fibonacci/26/01/01/0007/

TeX:

F_{n} = \frac{n}{{2}^{n - 1}} \,{}_2F_1\!\left(\frac{1 - n}{2}, \frac{2 - n}{2}, \frac{3}{2}, 5\right)

n \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`Fibonacci`	$F_{n}$	Fibonacci number
`Pow`	${a}^{b}$	Power
`Hypergeometric2F1`	$\,{}_2F_1\!\left(a, b, c, z\right)$	Gauss hypergeometric function
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("1c90fb"),
    Formula(Equal(Fibonacci(n), Mul(Div(n, Pow(2, Sub(n, 1))), Hypergeometric2F1(Div(Sub(1, n), 2), Div(Sub(2, n), 2), Div(3, 2), 5)))),
    Variables(n),
    Assumptions(Element(n, ZZ)),
    References("http://functions.wolfram.com/IntegerFunctions/Fibonacci/26/01/01/0007/"))

Topics using this entry

Fibonacci numbers

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