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In this note, we consider a generalized Fibonacci sequence $\{q_n\}$. Then give a connection between the sequence $\{q_n\}$ and the Chebyshev polynomials of the second kind $U_n(x)$. With the aid of factorization of Chebyshev polynomials of the second kind $U_n(x)$, we derive the complex factorizations of the sequence $\{q_n\}$.
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참고문헌 (12)
참고문헌 신청
A. F. Horadam / 1961 / A generalized Fibonacci sequences / Amer. Math. Monthly 68 : 455 ~ 459
A. Oteles / 2013 / Positive integer power of certain complex tridiago-nal matrices / Applied Mathematics and Computation 219 (21) : 10448 ~ 10455
D. Kalman / 2002 / The Fibonacci numbers - Exposed / The Mathematical Magazine 2
H. Zhang / 2013 / On the reciprocal sums of the generalized Fibonacci se-quences / Adv. Di er. Equ 377
H.J. Hsiao / 1984 / On factorization of Chebyshev's polynomials of the rst kind / Bulletin of the Institute of Mathematics Academia Sinica 12 (1) : 89 ~ 94
A. Oteles / 2013 / Positive integer power of certain complex tridiago-nal matrices / Applied Mathematics and Computation 219 (21) : 10448 ~ 10455
D. Kalman / 2002 / The Fibonacci numbers - Exposed / The Mathematical Magazine 2
H. Zhang / 2013 / On the reciprocal sums of the generalized Fibonacci se-quences / Adv. Di er. Equ 377
H.J. Hsiao / 1984 / On factorization of Chebyshev's polynomials of the rst kind / Bulletin of the Institute of Mathematics Academia Sinica 12 (1) : 89 ~ 94
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