“Lucas Polynomial Sequence”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lucas Polynomial Sequence

释义

Lucas Polynomial Sequence

A pair of generalized Polynomials which generalize the Lucas Sequence to Polynomials is given by

			(1)
			(2)

where

(3)

(4)

(5)

(Horadam 1996). Setting

gives

			(6)
			(7)

giving

			(8)
			(9)

The sequences most commonly considered have

, giving

			(10)
			(11)

Special cases are given in the following table.

		Polynomial 1	Polynomial 2
	1	Fibonacci	Lucas
	1	Pell	Pell-Lucas
1		Jacobsthal	Jacobsthal
		Fermat	Fermat-Lucas
		Chebyshev Polynomial of the Second Kind	Chebyshev Polynomial of the First Kind

See also Lucas Sequence

References

Horadam, A. F. ``Extension of a Synthesis for a Class of Polynomial Sequences.'' Fib. Quart. 34, 68-74, 1996.

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