Applications of certain probability distributions on positive integers

TL;DR

This paper explores the use of specific probability distributions on positive integers to generalize and analyze functions, employing advanced representations to extend existing mathematical frameworks.

Contribution

It introduces new generalizations of functions on positive integers using probability distributions and representation techniques, expanding the theoretical understanding of these functions.

Findings

New generalized functions on positive integers are proposed.

Representation methods enhance the modeling of these functions.

Theoretical insights into the properties of the generalized functions.

Abstract

The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $\pi_{\mathfrak p}$ from [22].