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LucasL

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LucasL[n]
gives the Lucas number L_n.
LucasL[n, x]
gives the Lucas polynomial L_n(x).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The L_n satisfy the recurrence relation L_n=L_(n-1)+L_(n-2) with L_1=1, L_2=3.
  • For any complex value of n the L_n are given by the general formula L_n=(phi^n+cos(pi n)phi^(-n)), where phi is the golden ratio.
  • The Lucas polynomial L_n(x) is the coefficient of t^n in the expansion of (2-t x)/(1-x t-t^2).
  • The Lucas polynomials satisfy the recurrence relation L_n(x)=x L_(n-1)(x)+L_(n-2)(x).
  • LucasL can be evaluated to arbitrary numerical precision.
  • LucasL automatically threads over lists.
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