# Asymptotic Expansions for the multiple gamma functions of Barnes-Milnor type

## TL;DR

This paper extends the asymptotic expansion formulas known for classical and Barnes' multiple gamma functions to a broader class of Barnes-Milnor type multiple gamma functions, enhancing understanding of their asymptotic behavior.

## Contribution

It provides new asymptotic expansion formulas specifically for Barnes-Milnor type multiple gamma functions, generalizing previous results.

## Key findings

- Derived asymptotic expansions for Barnes-Milnor gamma functions.
- Extended classical Stirling's formula to a broader class of functions.
- Enhanced mathematical understanding of the asymptotic properties of these functions.

## Abstract

The classical Stirling's formula gives the asymptotic behavior of the gamma function. Katayama and Ohtsuki generalized this formula for Barnes' multiple gamma functions. In this paper, we further generalize these formulas for the multiple gamma functions of BM (Barnes-Milnor) type.