# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Fibonacci

Fibonacci[n]
gives the Fibonacci number .

Fibonacci[n,x]
gives the Fibonacci polynomial .

## DetailsDetails

• Mathematical function, suitable for both symbolic and numerical manipulation.
• The satisfy the recurrence relation with .
• For any complex value of n, 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 nIntegers.
• Fibonacci can be evaluated to arbitrary numerical precision.
• Fibonacci automatically threads over lists.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

Compute Fibonacci numbers:

 Out[1]=