Romako63

Takagi's continuous nowhere differentiable function and binary digital sums ABSTRACT. In this paper we derive functional relations and explicit representations at dyadic points for Takagi's continuous nowhere differentiable function T and also for functions which are connected with T . As consequence we get formulas for binary digital sums, namely the Trollope-Delange formula for the number of ones, a formula counting the zeros as well as a formula for the alternating sum of digits. KEY WORDS. Takagi's continuous nowhere differentiable function, functional equations, Trollope-Delange formula for the sum-of-digits function, alternating sum of digits, Cantor sets