Corpus ID: 116200422

PELL AND PELL-LUCAS POLYNOMIALS

@inproceedings{Horadam1985PELLAP,
  title={PELL AND PELL-LUCAS POLYNOMIALS},
  author={A. F. Horadam and J. Mahon},
  year={1985}
}
The object of this paper is to record some properties of Pell polynomials Pn(x) and Veil-Lucas 'polynomials Qn(x) defined by the recurrence relations Pn+Z(x) = 2xPn + 1(x) + Pn(x) P0(x) = 0, P^x) = 1 (1.1) and Qn + 2(x) = 2xQn + l(x) + Qn(x) QQ(x) = 2, Q^x) = 2x. (1.2) Initially9 the polynomials are defined for n ^ 0 but their existence for n < 0 is readily extended, yielding P_n(x) = (-l)"Pn(aO (1.3) and Q_n(x) = (-l)Qn(x). (1.4) Some of these polynomials are: (P2(X) = 2x, P3(x) = kx + 1, Ph(x… Expand
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