On a new closed formula for the solution of second order linear difference equations and applications

2017/07/01 by Issam Kaddoura, Kaddoura, Issam, Bassam Mourad +1
Mathematics · Physics and Astronomy · #11B39 #65Q30 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1707.00179

openalex publication_date 2017/07/01 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28

Abstract

In this note, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in turn, gives new closed formulas concerning all sequences of this type such as the Fibonacci and Lucas sequences. As applications; we show that Binet's formula, in this case, is valid for negative integers as well. Finally, we find new summation formulas relating the elements of such sequences.

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