Fibonacci

Usage

• Fibonacci[n] gives the Fibonacci number .
• Fibonacci[n, x] gives the Fibonacci polynomial .

Notes

• 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 Section 3.2.6.

• Implementation notes: see Section A.9.4.

• See also: GoldenRatio.

• New in Version 3.

Further Examples