Takagi’s function and its functional equations

Abstract

The Takagi function T : R →R is given by

T(x) = ∑[∞][k=0] 1/2[k]d(2[k]x),

where d(y) denotes the distance from у to the nearest integer. We give some information on the history and on the analytic properties of T. Moreover, we present several functional equations for T and discuss various relationships between them as well as their characterizing properties.