On degenerate gamma functions

TL;DR

This paper explores the properties of degenerate gamma functions, including their analytic continuation, difference formulas, and integral representations, extending classical gamma function results to this new degenerate context.

Contribution

It provides a comprehensive analysis of degenerate gamma functions, including new formulas and representations, expanding the understanding of their mathematical properties.

Findings

Analytic continuation as a meromorphic function

Difference formula for degenerate gamma functions

Integral representation along a Hankel contour

Abstract

Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic function on the whole complex plane,the difference formula, the values at positive integers, some expressions following from the Weierstrass and Euler formulas for the usual gamma function and an integral representation as the integral along a Hankel contour.