| MSC: | 11A63 | Radix representation; digital problems {For metric results, see 11K16} |
| 39B22 | Equations for real functions [See also 26A51, 26B25] | |
| 26A30 | Singular functions, Cantor functions, functions with other special properties | |
| ZDM: | - | |
| CR: | - | |
| PACS: | - |
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.