Mathematical Problems in Engineering
Volume 2 (1996), Issue 5, Pages 393-400

Accommodation of zero-valued characteristic roots in the classical solution expression for linear, homogeneous, constant-coefficient difference equations

C. D. Johnson

Electrical and Computer Engineering Department, University of Alabama in Huntsville, Huntsville 35899, AL, USA

Received 3 August 1995

Copyright © 1996 C. D. Johnson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Linear, constant-coefficient difference equations play a central role in many areas of engineering, where cases involving repeated zero-valued characteristic roots are sometimes of particular interest. Unfortunately, the classical solution expression presented in the mathematical literature of difference equations is not valid for this latter case. In this paper we develop a unique generalization of the classical solution expression for linear, constant-coefficient, homogeneous difference equations that accommodates the most general case of repeated zero-valued characteristic roots, thereby “completing” the classical theory. A worked example is presented to illustrate our result.