On a new closed formula for the solution of second order linear difference equations and applications
Number Theory
2021-01-01 v3
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.
Cite
@article{arxiv.1707.00179,
title = {On a new closed formula for the solution of second order linear difference equations and applications},
author = {Issam Kaddoura and Bassam Mourad},
journal= {arXiv preprint arXiv:1707.00179},
year = {2021}
}
Comments
13 pages