A Note on Generating Functions for Hausdorff Moment Sequences

TL;DR

This paper investigates the behavior of the magnitude of functions with Taylor coefficients forming Hausdorff moment sequences along vertical lines in the complex plane.

Contribution

It provides new insights into the properties of functions whose Taylor coefficients are Hausdorff moment sequences, focusing on their behavior in the complex plane.

Findings

Characterization of the behavior of |f(γ+iy)| for functions with Hausdorff moment sequence coefficients

Analysis of the growth and decay properties of these functions along vertical lines

Potential implications for the theory of moment sequences and complex analysis

Abstract

For functions $f$ whose Taylor coefficients at the origin form a Hausdorff moment sequence we study the behaviour of $w(y):=|f(\gamma+iy)|$ for $y>0$ ($\gamma\leq1$ fixed).