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Fibonacci

Fibonacci[n]
gives the Fibonacci number F_n.
Fibonacci[n, x]
gives the Fibonacci polynomial F_n(x).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The F_n satisfy the recurrence relation F_n=F_(n-1)+F_(n-2) with F_1=F_2=1.
  • For any complex value of n the F_n are given by the general formula , where phi is the Golden Ratio.
  • The Fibonacci polynomial F_n(x) is the coefficient of t^n in the expansion of t/(1-xt-t^2).
  • The Fibonacci polynomials satisfy the recurrence relation F_n(x)=xF_(n-1)(x)+F_(n-2)(x).
  • 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.
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