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...

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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
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description 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.
doi_str_mv 10.1002/mma.5541
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subjects closed‐form formula
complex domain
Complex numbers
Difference equations
Domains
Mathematical analysis
solvability
title More on a hyperbolic‐cotangent class of difference equations
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