Wolfram Language & System 10.3 (2015)|Legacy Documentation

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gives the Fibonacci number .

gives the Fibonacci polynomial .


  • 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.
Introduced in 1996
| Updated in 1999