%0 Journal Article
%T The improper infinite derivatives of Takagi's nowhere-differentiable function
%A Pieter C. Allaart
%A Kiko Kawamura
%J Mathematics
%D 2010
%I arXiv
%X Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono, we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T'(x) is infinite have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained.
%U http://arxiv.org/abs/1002.2731v1