On the connection between tridiagonal matrices, Chebyshev polynomials, and Fibonacci numbers

[1] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth edition, Dover Publications, Inc., New York, 1970.Search in Google Scholar

[2] M. Andelić, Z. Du, C. M. da Fonseca, E. Kılıç, A matrix approach to some second-order difference equations with sign-alternating coefficients, J. Difference Equ. Appl., 26 (2020), 149–162.10.1080/10236198.2019.1709180Search in Google Scholar

[3] M. Anđelić, C. M. da Fonseca, A determinantal formula for generalized Fibonacci numbers, Matematiche (Catania), 74 (2019), 363–367.Search in Google Scholar

[4] G. B. Arfken, H. J. Weber, F. E. Harris, Mathematical Methods for Physicists: A Comprehensive Guide, Academic Press, Orlando, 1985.Search in Google Scholar

[5] R. G. Buschman, Fibonacci numbers, Chebyshev polynomials generalizations and difference equations, Fibonacci Quart. 1 (1963), 1–8, 19.Search in Google Scholar

[6] T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.Search in Google Scholar

[7] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht, Netherlands, 1974.Search in Google Scholar

[8] Erdélyi, et al., Higher Transcendental Functions, vol. 2, McGraw Hill, New York, 1953.Search in Google Scholar

[9] C. F. Fischer, R. A. Usmani, Properties of some tridiagonal matrices and their application to boundary value problems, SIAM J. Numer. Anal., 6 (1969), 127–141.10.1137/0706014Search in Google Scholar

[10] C. M. da Fonseca, J. Petronilho, Explicit inverses of some tridiagonal matrices, Linear Algebra Appl., 325 (2001), 7–21.10.1016/S0024-3795(00)00289-5Search in Google Scholar

[11] G. Heinig, K. Rost, Algebraic Methods for Toeplitz-Like Matrices and Operators, Birkhäuser OT 13, 1984.10.1515/9783112529003Search in Google Scholar

[12] A. F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3 (1965), 161–176.Search in Google Scholar

[13] F. Qi, V. Čerňanová, Y. S. Semenov, Some tridiagonal determinants related to central Delannoy numbers, the Chebyshev polynomials, and the Fibonacci polynomials, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 81 (2019), 123–136.Search in Google Scholar

[14] F. Qi, V. Čerňanová, X.-T. Shi, B.-N. Guo, Some properties of central Delannoy numbers, J. Comput. Appl. Math., 328 (2018), 101–115.10.1016/j.cam.2017.07.013Search in Google Scholar

[15] F. Qi, B.-N. Guo, Expressing the generalized Fibonacci polynomials in terms of a tridiagonal determinant, Matematiche (Catania), 72 (2017), 167–175.Search in Google Scholar

[16] F. Qi, A.-Q. Liu, Alternative proofs of some formulas for two tridiagonal determinants, Acta Univ. Sapientiae, Mathematica, 10 (2018), 287–297.Search in Google Scholar

[17] G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM J. Matrix Anal. Appl., 13 (1992), 707–728.10.1137/0613045Search in Google Scholar

[18] D. Moskovitz, The numerical solution of Laplace’s and Poisson’s equations, Quart. Appl. Math., 2 (1944), 14S–63.10.1090/qam/11186Search in Google Scholar

[19] P. Schlegel, The explicit inverse of a tridiagonal matrix, Math. Comp. 24 (1970), 665.10.1090/S0025-5718-1970-0273798-2Search in Google Scholar

[20] R. Usmani, Inversion of a tridiagonal Jabobi matrix, Linear Algebra Appl., 212/213 (1994), 413–414.10.1016/0024-3795(94)90414-6Search in Google Scholar

[21] T. Yamamoto, Y. Ikebe, Inversion of band matrices, Linear Algebra Appl., 24 (1979), 105–111.10.1016/0024-3795(79)90151-4Search in Google Scholar