Fungrim home page

Fungrim entry: 1c90fb

Fn=n2n12F1 ⁣(1n2,2n2,32,5)F_{n} = \frac{n}{{2}^{n - 1}} \,{}_2F_1\!\left(\frac{1 - n}{2}, \frac{2 - n}{2}, \frac{3}{2}, 5\right)
Assumptions:nZn \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
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
Hypergeometric2F12F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
ZZZ\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.

2019-08-19 14:38:23.809000 UTC