Asymptotic series and inequalities associated to some expressions involving the volume of the unit ball

TL;DR

This paper explores asymptotic series related to the volume of n-dimensional unit balls and presents improved classical inequalities with detailed proofs and methods.

Contribution

It introduces new asymptotic series and refined inequalities for the volume of the unit ball, with comprehensive proofs and methodological enhancements.

Findings

Asymptotic series for volume expressions derived

Improved classical inequalities established

Detailed proofs and methods provided

Abstract

The aim of this work is to expose some asymptotic series associated to some expressions involving the volume of the n-dimensional unit ball. All proofs and the methods used for improving the classical inequalities announced in the final part of the first section are presented in an extended form in a paper submitted by the author to a journal for publication.