Fibonacci

Fibonacci[n] gives the Fibonacci number .

Fibonacci[n, x] gives the Fibonacci polynomial .

Integer mathematical function (see Section A.3.10).

The satisfy the recurrence relation with .

For any complex value of the are given by the general formula , where is the golden ratio.

The Fibonacci polynomial is the coefficient of in the expansion of .

The Fibonacci polynomials satisfy the recurrence relation .

FullSimplify and FunctionExpand include transformation rules for combinations of Fibonacci numbers with symbolic arguments when the arguments are specified to be integers using n Integers.

See The Mathematica Book: Section 3.2.5.

Implementation Notes: see section A.9.4.

See also: GoldenRatio.

Further Examples