An elegant Multi-Integral that implies an even more elegant determinant identity of Dougherty and McCammond

TL;DR

This paper presents an explicit evaluation of a complex multi-variate integral and uses it to provide a concise proof of a notable determinant identity related to critical values, enhancing understanding in the field.

Contribution

It introduces a new explicit integral evaluation and offers a shorter proof of a known determinant identity, advancing mathematical techniques for such identities.

Findings

Explicit evaluation of a multi-variate integral

Shorter proof of Dougherty and McCammond's determinant identity

Enhanced understanding of critical value-related identities

Abstract

We state and prove an explicit evaluation of a certain multi-variate integral and use it to furnish a new, and shorter, proof of an elegant determinant identity of Michael Dougherty and Jon McCammond that came up in their study of critical values.