Pell and Pell–Lucas Numbers with Applications pp 255-281 | Cite as
Pell and Pell–Lucas Polynomials
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Abstract
Pell numbers and Pell–Lucas numbers are specific values of Pell polynomials p n (x) and Pell–Lucas polynomials q n (x), respectively. Both families were studied extensively in 1985 by A.F. Horadam of the University of New England, Armidale, Australia, and Bro. J.M. Mahon of the Catholic College of Education, Sydney, Australia [108]. Both families are often defined recursively: where n ≥ 3. The first ten Pell and Pell–Lucas polynomials are given in Table 14.1.
$$\displaystyle\begin{array}{rcl} \begin{array}{llllllllll} p_{0}(x) & =&0,p_{1}(x) = 1 &&&&&q_{0}(x) & =&2,q_{1}(x) = 2x \\ p_{n}(x)& =&2xp_{n-1}(x) + p_{n-2}(x);&&&&&q_{n}(x)& =&2xq_{n-1}(x) + q_{n-2}(x),\end{array} & & {}\\ \end{array}$$
References
- 73.A. Dorp, Problem B-891, Fibonacci Quarterly 38 (2000), 85.Google Scholar
- 91.N. Gauthier, Problem H-720, Fibonacci quarterly 50 (2012), 280.MathSciNetGoogle Scholar
- 102.V.E. Hoggatt, Jr. Fibonacci and Lucas Numbers, The Fibonacci Association, Santa Clara, CA, 1969.MATHGoogle Scholar
- 108.A.F. Horadam and Bro. J.M. Mahon, Pell and Pell–Lucas Polynomials, Fibonacci Quarterly 23 (1985), 7–20.Google Scholar
- 126.T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley, New York, 2001.CrossRefMATHGoogle Scholar
- 211.H.-E. Seiffert, Problem H-548, Fibonacci Quarterly 37 (1999), 91.Google Scholar
- 212.H.-E. Seiffert, Solution to Problem H-548, Fibonacci Quarterly 38 (2000), 189–191.Google Scholar
- 213.H.-E. Seiffert, Problem B-902, Fibonacci Quarterly 38 (2000), 372.Google Scholar
- 214.H.-E. Seiffert, Solution to Problem B-891, Fibonacci Quarterly 38 (2000), 470–471.Google Scholar
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