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

Abstract

In this note, we recall several connections between the determinant of some tridiagonal matrices and the orthogonal polynomials allowing the relation between Chebyshev polynomials of second kind and Fibonacci numbers. With basic transformations, we are able to recover some recent results on this matter, bringing them into one place.

Keywords

• tridiagonal matrices
• chebyshev polynomials of second kind
• determinant
• fibonacci numbers
• 11b37
• 11b39
• 15a15
• 15b05
• 15b36
• 39a10
• 42c05