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Fungrim entry: 70878b

Fm+n1=FmFn+Fm1Fn1F_{m + n - 1} = F_{m} F_{n} + F_{m - 1} F_{n - 1}
Assumptions:mZandnZm \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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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC