On Asymptotics Of \Gamma_{q}(z) As q Approaching 1

TL;DR

This paper derives the main asymptotic behavior of the q-Gamma function as q approaches 1, providing a formula valid across the complex plane except at the poles of the classical Gamma function.

Contribution

It offers a new derivation of the asymptotic main term for the q-Gamma function near q=1, extending understanding of its behavior in the complex plane.

Findings

Asymptotic formula valid for all complex z except poles

Derivation applicable as q approaches 1 from below

Clarifies the relationship between q-Gamma and classical Gamma functions

Abstract

In this note we give a derivation of the asymptotic main term for the q-Gamma function as q approaching 1. This formula is valid on all the complex plan except at the poles of the Euler Gamma function.