Lambert Series, the Arithmetic Function \(r(n)\) and Gauss’s Probability Integral

In this article we will study some properties of Lambert series. Then, using Lambert series relative to the representation of integers as sum of two squares, we will compute the value of Gauss’s classical probability integral. 1) Dirichlet generating functions Let’s briefly recall some properties of Dirichlet generating functions. Definition 1.1Given Read more…

Iterated Function Systems, Fractals and Sierpinski Triangle

In a previous article we have introduced some examples of fractals, illustrating their main characteristics, both qualitative and quantitative: self-similarity, geometric irregularity, fractional dimension. To continue the study of fractal science, it’s first necessary to give a more rigorous definition of the mathematical context in which fractal objects are defined.Each Read more…