GAMMA 函 數 的 性 質

性質1

 證明 :   GAMMA函數的定義為 

             , 利用分部積分法

           

                                                   

                                                   

                                                  

性質2  GAMMA函數可以利用變數變換而得到許多不同的表現形式

                           (1)

                           (2)

                           (3)

性質3  

證明:               令

           

           考慮           

                   積分區域為第一象限 , 現在改為極座標

                                                          

                                                          

            故    ,  故

性質4  

 證明:    因為                  

                                                                    

                                                                    

                                                                    

                    上下同乘 即可得到性質4