Gamma

Gamma[z]

is the Euler gamma function .

Gamma[a,z]

is the incomplete gamma function .

Gamma[a,z0,z1]

is the generalized incomplete gamma function .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The gamma function satisfies .
  • The incomplete gamma function satisfies .
  • The generalized incomplete gamma function is given by the integral .
  • Note that the arguments in the incomplete form of Gamma are arranged differently from those in the incomplete form of Beta.
  • Gamma[z] has no branch cut discontinuities.
  • Gamma[a,z] has a branch cut discontinuity in the complex z plane running from to .
  • For certain special arguments, Gamma automatically evaluates to exact values.
  • Gamma can be evaluated to arbitrary numerical precision.
  • Gamma automatically threads over lists.

Examples

open all close all

Basic Examples  (4)

Integer values:

In[1]:=
Click for copyable input
Out[1]=

Half-integer values:

In[1]:=
Click for copyable input
Out[1]=

Evaluate numerically for complex arguments:

In[1]:=
Click for copyable input
Out[1]=
In[1]:=
Click for copyable input
Out[1]=

Scope  (44)

Generalizations & Extensions  (6)

Applications  (5)

Properties & Relations  (7)

Possible Issues  (2)

Neat Examples  (2)

Introduced in 1988
(1.0)