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Alternative proofs of some formulas for two tridiagonal determinants. (English) Zbl 07042987

Summary: In the paper, the authors provide five alternative proofs of two formulas for a tridiagonal determinant, supply a detailed proof of the inverse of the corresponding tridiagonal matrix, and provide a proof for a formula of another tridiagonal determinant. This is a companion of the paper [F. Qi, V. Čerňanová,and 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), in press.

MSC:

47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B83 Special sequences and polynomials
11C08 Polynomials in number theory
11C20 Matrices, determinants in number theory
11Y55 Calculation of integer sequences
15B36 Matrices of integers
26C99 Polynomials, rational functions in real analysis
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References:

[1] C.-P. Chen, A.-Q. Liu, and F. Qi, Proofs for the limit of ratios of consecutive terms in Fibonacci sequence, Cubo Mat. Educ. 5 (3) (2003), 23-30.; · Zbl 1162.11312
[2] G. Y. Hu and R. F. O’Connell, Analytical inversion of symmetric tridiagonal matrices, J. Phys. A 29 (7) (1996), 1511-1513; Available online at .; · Zbl 0914.15002
[3] F. Qi and B.-N. Guo, The reciprocal of the weighted geometric mean is a Stieltjes function, Bol. Soc. Mat. Mex. (3) 24 (1) (2018), 181-202; Available online at .; · Zbl 1390.30048
[4] F. Qi and V. Čerňanová, Some discussions on a kind of improper integrals, Int. J. Anal. Appl. 11 (2) (2016), 101-109.; · Zbl 1379.26015
[5] F. Qi, V. Čerňanová, and Y. S. Semenov, On tridiagonal determinants and the Cauchy product of central Delannoy numbers, ResearchGate Working Paper (2016), available online at .; · Zbl 1513.11057
[6] F. Qi, V. Čerňanová,and 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), in press.; · Zbl 1513.11057
[7] F. Qi, V. Čerňanová, X.-T. Shi, and B.-N. Guo, Some properties of central Delannoy numbers, J. Comput. Appl. Math. 328 (2018), 101-115; Available online at .; · Zbl 1371.11161
[8] F. Qi and B.-N. Guo, Expressing the generalized Fibonacci polynomials in terms of a tridiagonal determinant, Matematiche (Catania) 72 (1) (2017), 167-175; Available online at .; · Zbl 1432.11014
[9] F. Qi, D.-W. Niu, and D. Lim, Notes on the Rodrigues formulas for two kinds of the Chebyshev polynomials, HAL archives (2018), available online at .;
[10] F. Qi, X.-T. Shi, and B.-N. Guo, Some properties of the Schröder numbers, Indian J. Pure Appl. Math. 47 (4) (2016), 717-732; Available online at .; · Zbl 1365.05018
[11] F. Qi, Q. Zou, and B.-N. Guo, Some identities and a matrix inverse related to the Chebyshev polynomials of the second kind and the Catalan numbers, Preprints 2017, 2017030209, 25 pages; Available online at .;
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