(untitled) (Analysis in Theory and Applications, 2020)
It was proved by Shen that the graph of the classical Weierstrass function _n=0^∞ λ^n (2π b^n x) has Hausdorff dimension 2+λ/b, for every integer b≥ 2 and every λ(1/b,1) [Hausdorff dimension of the graph of the classical Weierstrass functions, Math. Z., 289 (2018), 223–266]. In this paper, we prove that the dimension formula holds for every integer b≥ 3 and every λ(1/b,1) if we replace the function by in the definition of Weierstrass function. A class of more general functions are also discussed.