TL;DR
This paper introduces a new class of determinants that unify various mathematical objects and provides a closed-form formula for terms of linear recurrence relations based on initial conditions and coefficients.
Contribution
It presents a novel class of determinants linking diverse mathematical objects and derives a closed formula for linear recurrence terms.
Findings
Unified representation of Fibonacci, Lucas, Tchebychev, Hermite, Laguerre, Legendre polynomials as determinants
Derived a closed formula for arbitrary terms of linear recurrence equations
Established connections between determinants and classical mathematical objects
Abstract
A class of determinants is introduced. Different kind of mathematical objects, such as Fibonacci, Lucas, Tchebychev, Hermite, Laguerre, Legendre polynomials, sums and covergents are represented as determinants from this class. A closed formula in which arbitrary term of a homogenous linear recurrence equation is expressed in terms of the initial conditions and the coefficients is proved.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Fractional Differential Equations Solutions · Nonlinear Differential Equations Analysis