gives the Lucas number .

gives the Lucas 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 Lucas polynomial is the coefficient of in the expansion of .
  • The Lucas polynomials satisfy the recurrence relation .
  • LucasL can be evaluated to arbitrary numerical precision.
  • LucasL automatically threads over lists.
Introduced in 2007
| Updated in 2008
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