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Gamma

Usage

Gamma[z]用来给出Euler伽马函数  .
Gamma[a, z] 用来给出不完全伽马函数  .
Gamma[a,  ,  ] 用来给出广义不完全伽马函数  .


Notes

• 数学函数(参见 A.3.10节).
• 伽马函数满足  .
• 不完全伽马函数满足 .
• 广义不完全伽马函数由积分  给出.
• 注意, Gamma 的不完全形式中的参数与Beta的不完全形式中的不同.
Gamma[z] 没有不连续分支线.
Gamma[a, z]在复平面上从  到0具有一条不连续分支线.
• Fullsimlify和FunctionExpand包含Gamma的变换法则.
• 参见Mathematica全书: 3.2.10节.
• 实现注释:参见A.9.4.节.
Further Examples

Here are the first 10 integer values of the gamma function; these are the factorials offset by 1.

In[1]:=  

Out[1]=

The gamma function generalizes factorials to numbers beyond the positive integers.

In[2]:=  

Out[2]=

This is the derivative.

In[3]:=  

Out[3]=

This is a series expansion around  .

In[4]:=  

Out[4]=



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