Asymptotic Properties of Stieltjes Constants

TL;DR

This paper introduces a new, simpler, and more accurate asymptotic formula for Stieltjes constants, facilitating deeper analysis of their intriguing regularities.

Contribution

It provides a novel asymptotic formula for Stieltjes constants that improves upon previous methods in simplicity and accuracy.

Findings

New asymptotic formula for Stieltjes constants

Enhanced understanding of regularities in these constants

Potential for further analytical developments

Abstract

We present a new asymptotic formula for the Stieltjes constants which is both simpler and more accurate than several others published in the literature (see e.g. \cite{Fekih-Ahmed}, \cite{Knessl Coffey}, \cite{Paris}). More importantly, it is also a good starting point for a detailed analysis of some surprising regularities in these important constants.