A Survey of Properties of Third Order Pell Diagonal Functions

Br. J. M. Mahon and A. F. Horadam

A chapter in Applications of Fibonacci Numbers, 1990, pp 255-271 from Springer

Abstract: Abstract This paper is concerned with the simpler properties of some third order sequences of polynomials. These sequences are {r n (x)}, {s n (x)} and {t n (x)}, defined thus: (1.1) $$\left. {\begin{array}{*{20}{c}} {{r_o}\left( x \right) = 0,{r_1}\left( x \right) = 1,{r_2}\left( x \right) = 2x} \\ {{r_{n + 1}}\left( x \right) = 2x{r_n}\left( x \right) + {r_{n - 2}}\left( x \right)\left( {n \geqslant 2} \right)} \end{array}} \right\},$$ (1.2) $$\left. {\begin{array}{*{20}{c}} {{s_o}\left( x \right) = 0,{s_1}\left( x \right) = 2,{s_2}\left( x \right) = 2x} \\ {{s_{n + 1}}\left( x \right) = 2x{s_n}\left( x \right) + {s_{n - 2}}\left( x \right)\left( {n \geqslant 2} \right)} \end{array}} \right\},$$ (1.3) $$\left. {\begin{array}{*{20}{c}} {{t_o}\left( x \right) = 3,{t_1}\left( x \right) = 2x,{t_2}\left( x \right) = 4{x^2}} \\ {{t_{n + 1}}\left( x \right) = 2x{t_n}\left( x \right) + {t_{n - 2}}\left( x \right)\left( {n \geqslant 2} \right)} \end{array}} \right\}.$$

Keywords: Chebyshev Polynomial; Order Sequence; Fibonacci Number; Auxiliary Equation; Complex Cube (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-94-009-1910-5_29

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