Functional equations characterizing the tangent function over a convex polygon

In 2004, Benz, affirming an earlier result of Davison, proved that for the three angles x , y , z of a non-degenerate triangle, the functional equation f ( x ) f ( y ) f ( z ) =  f ( x ) +  f ( y ) +  f ( z ) characterizes the tangent function. We generalize this result by exhibiting a functional eq...

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Published inAequationes mathematicae Vol. 88; no. 3; pp. 201 - 210
Main Authors Hengkrawit, Charinthip, Laohakosol, Vichian, Ponpetch, Kanet
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.12.2014
Springer Nature B.V
Subjects
Analysis
Combinatorics
Functions (mathematics)
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Polygons
Tangents
Triangles
39B05
tangent function
39B22
Functional equation
gon
non-degenerate convex
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Summary:In 2004, Benz, affirming an earlier result of Davison, proved that for the three angles x , y , z of a non-degenerate triangle, the functional equation f ( x ) f ( y ) f ( z ) =  f ( x ) +  f ( y ) +  f ( z ) characterizes the tangent function. We generalize this result by exhibiting a functional equation, with n parameters representing the angles of a non-degenerate convex n -gon, which characterizes the tangent function.
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ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-013-0229-3