关于Γ函数三个定义等价性的证明

Proof on the equivalence of the three definitions of the Gamma function

Γ函数在历史上最典型的定义是由Euler,Gauss,Weierstrass等分别使用含参变量积分及无穷乘积定义的,但这三种方式本质是等价的,本文将使用Bohr-Mollerup定理给出这三个定义的等价性的一个简短证明.

In history,the definitions of the Gamma function were given by Euler, Gauss and Weierstrass. In this paper, we show that they are equivalent.