Fungrim home page

Fungrim entry: d0d91a

n=0Fnznn!=25ez/2sinh ⁣(52z)\sum_{n=0}^{\infty} F_{n} \frac{{z}^{n}}{n !} = \frac{2}{\sqrt{5}} {e}^{z / 2} \sinh\!\left(\frac{\sqrt{5}}{2} z\right)
Assumptions:zCz \in \mathbb{C}
\sum_{n=0}^{\infty} F_{n} \frac{{z}^{n}}{n !} = \frac{2}{\sqrt{5}} {e}^{z / 2} \sinh\!\left(\frac{\sqrt{5}}{2} z\right)

z \in \mathbb{C}
Fungrim symbol Notation Short description
Sumnf(n)\sum_{n} f(n) Sum
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
Sqrtz\sqrt{z} Principal square root
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Sum(Mul(Fibonacci(n), Div(Pow(z, n), Factorial(n))), For(n, 0, Infinity)), Mul(Mul(Div(2, Sqrt(5)), Exp(Div(z, 2))), Sinh(Mul(Div(Sqrt(5), 2), z))))),
    Assumptions(Element(z, CC)))

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