Authors: Stević, Stevo 
Iričanin, Bratislav
Kosmala, Witold
Šmarda, Zdeněk
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Note on theoretical and practical solvability of a class of discrete equations generalizing the hyperbolic-cotangent class
Journal: Journal of Inequalities and Applications
Issue Date: 17-Nov-2021
Rank: ~M21a
ISSN: 1029-242X
DOI: 10.1186/s13660-021-02720-w
There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied. We show that there is a class of theoretically solvable difference equations generalizing the hyperbolic-cotangent one. Our analysis shows a bit unexpected fact, namely that the solvability of the class is based on some algebraic relations, not closely related to some trigonometric ones, which enable us to solve them in an elegant way. Some examples of the difference equations belonging to the class which are practically solvable are presented, as well as some interesting comments on connections of the equations with some iteration processes.
Keywords: Difference equation | Equations solvable in a closed form | Practical solvability | Theoretical solvability
Publisher: Springer Link

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