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Abstract
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.
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1 Mathematical Institute of the Serbian Academy of Sciences, Beograd, Serbia (GRID:grid.419269.1) (ISNI:0000 0001 2146 2771); China Medical University, Department of Medical Research, China Medical University Hospital, Taichung, Taiwan, Republic of China (GRID:grid.254145.3) (ISNI:0000 0001 0083 6092)
2 Belgrade University, Faculty of Electrical Engineering, Beograd, Serbia (GRID:grid.7149.b) (ISNI:0000 0001 2166 9385); University of Kragujevac, Faculty of Mechanical and Civil Engineering in Kraljevo, Kraljevo, Serbia (GRID:grid.413004.2) (ISNI:0000 0000 8615 0106)
3 Appalachian State University, Deptartment of Mathematical Sciences, Boone, USA (GRID:grid.252323.7) (ISNI:0000 0001 2179 3802)
4 Brno University of Technology, Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno, Czech Republic (GRID:grid.4994.0) (ISNI:0000 0001 0118 0988)