More on a hyperbolic‐cotangent class of difference equations

We present a natural method for solving the difference equation xn=xn−kxn−l+axn−k+xn−l,n∈N0, where k,l∈N, parameter a, and initial values x−j, j=1,t‾, t=max{k,l}, are real or complex numbers. As a concrete example, the case k = 1, l = 2 is studied in detail, and several interesting formulas for solu...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2019-06, Vol.42 (9), p.2974-2992
Main Authors: Stević, Stevo, Iričanin, Bratislav, Kosmala, Witold
Format: Article
Language:English
Subjects:
closed‐form formula
complex domain
Complex numbers
Difference equations
Domains
Mathematical analysis
solvability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a natural method for solving the difference equation xn=xn−kxn−l+axn−k+xn−l,n∈N0, where k,l∈N, parameter a, and initial values x−j, j=1,t‾, t=max{k,l}, are real or complex numbers. As a concrete example, the case k = 1, l = 2 is studied in detail, and several interesting formulas for solutions and objects used in the analysis of the equation are given. A useful remark on solvability of difference equations on complex domains is presented and used here.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5541