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

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