Functional equations characterizing the tangent function over a convex polygon
The authors generalize a result of \textit{T. Davison} [``Report of meeting 40th international symposium on functional equations'', ibid. 65, No. 3, 292 (2003)] and \textit{W. Benz} [Aequationes Math. 68, No. 1--2, 117--120 (2004; Zbl 1055.39036)] characterizing the tangent function. The Davison-Benz theorem solves a conditional functional equation involving three variables which can be interpreted as the angles of a non-degenerate triangle. The authors generalize this result to the case of \(n(\geq 3)\) variables which can serve as the angles of a non-degenerate convex \(n\)-gon.
scientific article; zbMATH DE number 6380866