Abstract

Recently, the degenerate gamma functions were introduced as a degenerate version of the usual gamma function. In this paper, we investigate several properties of these functions. 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 ordinary gamma function, and an integral representation as an integral along a Hankel contour.

中文翻译：

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关于简并伽玛函数的注意

摘要

最近，简并伽马函数被引入为常规伽马函数的简并版本。在本文中，我们研究了这些功能的几种特性。即，我们获得了一个解析连续体，它是整个复平面上的亚纯函数，差分公式，正整数值，一些遵循普通伽玛函数的Weierstrass和Euler公式的表达式以及作为积分的整数表示汉克尔轮廓。