Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials

TL;DR

This paper surveys Apostol-Bernoulli functions and explores their connections to Eulerian and derivative polynomials, highlighting integral representations and their mathematical significance.

Contribution

It provides a comprehensive overview of Apostol-Bernoulli functions and their relationships to other polynomial families, emphasizing their integral representations.

Findings

Apostol-Bernoulli functions are closely related to Eulerian and derivative polynomials.

Integral representations offer insights into the properties of these functions.

The survey clarifies the mathematical significance of these functions in polynomial theory.

Abstract

This is a short survey of a class of functions introduces by Tom Apostol. The survey is focused on their relation to Eulerian polynomials, derivative polynomials, and also on some integral representations.