THE WEIERSTRASS FUNCTION AND <i>R/ φ</i> -FEATURES
The paper presents an approach to the study of non-differentiable functions. The basic idea is to use r/φ-algorithm proposed for the summation of divergent continued fractions. A modification of the Weierstrass function was introduced. It is called «Weierstrass function on the interval». This function is not defined by the value function at a point x of an infinite interval, as it is in the classical case, but as a set of values of the Weierstrass points uniformly distributed over a fixed time interval [x <sub>0</sub>, x <sub>0</sub> + D]. Weierstrass functions are introduced for r/φ-characteristics. Examples of characteristics calculations were provided. The «limits» r/φ-characteristics for the Weierstrass function were found. It was determined that in the interval D, tends to zero, r-Weierstrass function characteristics coincide with the value of the modulus of the Weierstrass point x <sub>0</sub>, which establishes the limit of the function. When averaged φ-values characteristics obtained at various intervals for D ® 0, we obtained the "marginal” φ-characteristic. It was experimentally established the continuity of the Weierstrass function in the classical sense.