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Fungrim entry: 70878b

Fm+n−1=FmFn+Fm−1Fn−1F_{m + n - 1} = F_{m} F_{n} + F_{m - 1} F_{n - 1}
Assumptions:m∈Z  and⁡  n∈Zm \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
F_{m + n - 1} = F_{m} F_{n} + F_{m - 1} F_{n - 1}

m \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
FibonacciFnF_{n} Fibonacci number
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("70878b"),
    Formula(Equal(Fibonacci(Sub(Add(m, n), 1)), Add(Mul(Fibonacci(m), Fibonacci(n)), Mul(Fibonacci(Sub(m, 1)), Fibonacci(Sub(n, 1)))))),
    Variables(m, n),
    Assumptions(And(Element(m, ZZ), Element(n, ZZ))))

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2021-03-15 19:12:00.328586 UTC