On compact representations for the solutions of linear difference equations with variable coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:318

Article

Abderraman Marrero, J.¹  Tomeo, V.² 

[1] UPM Tech Univ Madrid, Sch Telecommun Engn, Dept Math Appl Informat Technol, Avda Complutense S-N,Ciudad Univ, Madrid 28040, Spain

[2] Univ Complutense, Fac Stat Studies, Dept Algebra, Avda Puerta Hierro S-N,Ciudad Univ, E-28040 Madrid, Spain

关键词: Enumerative combinatorics;    Hessenbergian;    Linear difference equation;    Nested sum;   

DOI  :  10.1016/j.cam.2016.02.049

来源: Elsevier

【 摘 要 】

A comprehensive treatment on compact representations for the solutions of linear difference equations with variable coefficients, of both nth and unbounded order, is presented. The equivalence between their celebrated combinatorial and determinantal representations is considered. A corresponding representation is proposed using determined nested sums of their variable coefficients. It makes explicit all the sum of products involved in the previous representations of such solutions. Some basic applications are also illustrated. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free