Tridiagonal matrices representations of generalized bivariate complex polynomials Generalized bivariate complex polynomials
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Abstract
This paper introduces a closed-form expression for generalized bivariate complex polynomials using a tridiagonal determinant in symbolic form. Subsequences with even and odd indices are also represented as tridiagonal determinants. Furthermore, we achieve factorizations of the tridiagonal determinant in terms of eigenvalues and demonstrate the versatility of the established closed-form formula through its application in deriving Chebyshev polynomials. This generalized sequence encompasses several well-known polynomial families in one or two variables, including the Fibonacci, Lucas, Pell, Pell–Lucas, and Chebyshev polynomial sequences in tridiagonal representation. Finally, we explore identities involving complex bivariate generalized polynomials, expressed as second-order determinants.
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