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Fungrim entry: 05209f

∑n=0∞Fnzn=z1−z−z2\sum_{n=0}^{\infty} F_{n} {z}^{n} = \frac{z}{1 - z - {z}^{2}}
Assumptions:z∈C  and⁡  ∣z∣<φ−1z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < \varphi - 1
TeX:
\sum_{n=0}^{\infty} F_{n} {z}^{n} = \frac{z}{1 - z - {z}^{2}}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|z\right| < \varphi - 1
Definitions:
Fungrim symbol Notation Short description
Sum∑nf(n)\sum_{n} f(n) Sum
FibonacciFnF_{n} Fibonacci number
Powab{a}^{b} Power
Infinity∞\infty Positive infinity
CCC\mathbb{C} Complex numbers
Abs∣z∣\left|z\right| Absolute value
GoldenRatioφ\varphi The golden ratio (1.618...)
Source code for this entry:
Entry(ID("05209f"),
    Formula(Equal(Sum(Mul(Fibonacci(n), Pow(z, n)), For(n, 0, Infinity)), Div(z, Sub(Sub(1, z), Pow(z, 2))))),
    Variables(z),
    Assumptions(And(Element(z, CC), Less(Abs(z), Sub(GoldenRatio, 1)))))

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2021-03-15 19:12:00.328586 UTC