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.