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Abstract
We use the Z-transform to motivate the Baldoni et al algorithm to solve homogeneous linear recurrence relations, with applications to Fibonacci numbers and Chebyshev polynomials.
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References
M. W. Baldoni, C. Ciliberto, G. M. Piacentini Cattaneo, Elementary number theory, cryptography and codes, Springer, Berlin (2009).
P. Lam-Estrada, J. López-Bonilla, R. López-Vázquez, Baldoni et al method for homogeneous linear recurrence relations, Proc. Int. Conf. on Special Functions & Applications, ICSFA 2015, Amity University, Noida, Uttar Pradesh, India, Sept. 10-12, 2015, pp. 6-10.
L. Brand, The companion matrix and its properties, Am. Math. Monthly 71, No. 6 (1964) 629-634.
J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford (1965).
R. A. Horn, Ch. R. Johnson, Matrix analysis, Cambridge University Press (2013).
I. Guerrero-Moreno, J. López-Bonilla, J. Rivera-Rebolledo, Leverrier-Takeno coefficients for the characteristic polynomial of a matrix, J. Inst. Eng. (Nepal) 8, No. 1-2 (2011) 25-258.
J. López-Bonilla, S. Vidal-Beltrán, A. Zúñiga-Segundo, Characteristic equation of a matrix via Bell polynomials, Asia Matematika 2, No. 2 (2018) 49-51.
H. Torres-Silva, J. López-Bonilla, S. Vidal-Beltrán, On the Faddeev-Sominsky’s algorithm, World Scientific News 106 (2018) 238-244.
J. López-Bonilla, R. López-Vázquez, S. Vidal-Beltrán, Coefficients of the characteristic polynomial, African J. Basic & Appl. Sci. 11, No. 1 (2019) 22-24.
J. D. Bulnes, N. Islam, J. López-Bonilla, Leverrier-Takeno and Faddeev-Sominsky algorithms, Scientia Magna 17, No. 1 (2022) 77-84.
L. Debnath, D. Bhatta, Integral transforms and their applications, Chapman & Hall / CRC, New York (2007) Chap. 12.
B. Patra, An introduction to integral transforms, CRC Press, Boca Raton, Fl, USA (2018) Chap. 14.
P. L. Chebyshev, Théorie des mécanismes connus sous le nom de parallélogrammes, Mém. Acad. Sci. Pétersb. 7 (1854) 539-568.
C. Lanczos, Applied analysis, Dover, New York (1988) Chap. 3.
J. C. Mason, D. C. Handscomb, Chebyshev polynomials, Chapman & Hall / CRC, London (2002).
L. Pisano [Fibonacci], Liber Abaci (1202). R. A. Dunlap, The golden ratio and Fibonacci numbers, World Scientific, Singapore (1997).
S. Vajda, Fibonacci and Lucas numbers and the golden ratio section: Theory and applications, Dover,New York (2008).
P. Lam-Estrada, J. López-Bonilla, S. Yáñez-San Agustín, Hypergeometric form of the k-Fibonacci numbers, Prespacetime J. 7, No. 11 (2016) 1558-1560.
R. V. Churchill, Complex variables and applications, McGraw-Hill, London (1960).
B. G. S. Doman, The classical orthogonal polynomials, World Scientific, Singapore (2016).
C. Lanczos, Trigonometric interpolation of empirical and analytical functions, J. Math. Phys. 17 (1938) 123-199.
B. K. P. Scaife, Studies in numerical analysis, Academic Press, New York (1974).
J. H. Caltenco, J. López-Bonilla, J. Morales, G. Pérez-Teruel, Polynomial solutions of differential equations, Int. J. Eng. Sci. 2 (2014) 73-79.
K. Dilcher, Hypergeometric functions and Fibonacci numbers, Fibonacci Quart. 38, No. 4 (2000) 342-363.
E. Lucas, Théorie des nombres, Gauthier-Villars (1891).