Wolfram mathematica 未使用Mathematica验证基本Gamma函数身份

Mathematica V10不会将

True

返回到以下代码行：

Simplify[Gamma[z] == (z - 1)!, Element[z, Integers] && z > 0]
Simplify[(Gamma[1 - z] Gamma[z]) == Pi/Sin[ Pi z] , 
         Element[z, Complexes] && (0 < Re[z] < 1)]

它返回

True

您必须改用：

FullSimplify[Gamma[z]==（z-1）！，元素[z，整数]&&z>0]
FullSimplify[（Gamma[1-z]Gamma[z]）==Pi/Sin[Pi z]，
元素[z，复合物]&（0

FullSimplify

执行更多转换，如中所述

 Simplify[Abs[x] == x, x > 0]

FullSimplify[Gamma[z] == (z - 1)!, Element[z, Integers] && z > 0]
FullSimplify[(Gamma[1 - z] Gamma[z]) == Pi/Sin[ Pi z] , 
             Element[z, Complexes] && (0 < Re[z] < 1)]