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 equation, with n parameters representing the angles of a non-degenerate convex n-gon, which characterizes the tangent function.
Mathematics Subject Classification (2000)39B05 39B22
KeywordsFunctional equation tangent function non-degenerate convex n-gon
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