On polynomials of binomial type, exponential integral and the inverse logarithmic derivative eigenproblem

TL;DR

This paper investigates the properties of polynomials of binomial type and their extensions to complex indices, focusing on the transformation T related to the inverse logarithmic derivative eigenproblem, advancing understanding of their analytical structure.

Contribution

It introduces a detailed analysis of the transformation T and its action on formal power series, extending the theory of binomial type polynomials to complex indices and exploring related eigenproblems.

Findings

Characterization of the transformation T on formal power series

Extension of binomial type polynomials to complex indices

Insights into the inverse logarithmic derivative eigenproblem

Abstract

In this work we continue to study the properties of polynomials of binomial type and their canonical continuations to the complex index by exploring the properties of transformation T:=1/dlog which acts on formal power series $f(x)$ of the form $x+x^2\mathbb{C}[[x]]$.