Fibonacci

Fibonacci[n]

gives the Fibonacci number .

Fibonacci[n,x]

gives the Fibonacci polynomial .

Details

  • 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.

Examples

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Basic Examples  (1)

Compute Fibonacci numbers:

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Scope  (7)

Generalizations & Extensions  (2)

Applications  (13)

Properties & Relations  (15)

Possible Issues  (3)

Neat Examples  (8)

See Also

GoldenRatio  LucasL  RSolve  LinearRecurrence  RecurrenceTable  DifferenceRoot  GoldenAngle

Tutorials

Introduced in 1996
(3.0)
| Updated in 1999
(4.0)