An asymptotically sharp form of Ball's integral inequality

TL;DR

This paper determines the second order term in the asymptotic expansion of Ball's integral inequality and introduces a method to compute any term, also extending to a generalized form.

Contribution

It provides a novel method for computing the full asymptotic expansion of Ball's integral inequality and its generalizations.

Findings

Second order term in asymptotic expansion determined

Method to compute any term in the expansion introduced

Extension to generalized Ball's integral inequality

Abstract

We solve the open problem of determining the second order term in the asymptotic expansion of the integral in Ball's integral inequality. In fact, we provide a method by which one can compute any term in the expansion. We also indicate how to derive an asymptotically sharp form of a generalized Ball's integral inequality.