On convolution powers of 1/x

TL;DR

This paper investigates the convolution powers of the function 1/x, deriving functions that satisfy a recurrence relation, and provides a characterization and analysis of these solutions.

Contribution

It introduces a new framework for understanding convolution powers of 1/x through recurrence relations and their solutions.

Findings

Solutions are explicitly characterized.

Recurrence relations simplify analysis.

Provides insights into convolution powers of 1/x.

Abstract

Convolution powers of $1/x$ are transformed into functions $f_n$, which satisfy a simple recurrence relation. Solutions are characterized and analyzed.