The general solution of the linear difference equation of degree-2 and the continued fraction produced from this equation

TL;DR

This paper presents the general solution to second-degree linear difference equations and applies it to expand continued fractions into series, providing new insights into their structure and convergence.

Contribution

It introduces the first general solution for second-degree linear difference equations and applies it to continued fraction expansions, which was previously only partially addressed.

Findings

Derived the general solution for second-degree linear difference equations.

Applied the solution to expand continued fractions into series.

Provided new proofs and insights into continued fraction representations.

Abstract

In this article we give, for the fist time the solution of the general difference equation of 2-degree. We also give as application the expansion of a continued fraction into series, which was first proved, found in the past by the author.