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Factorial
LogGamma
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Gamma Functions and Related Functions
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Gamma
Gamma
[
z
]
is the Euler gamma function
.
Gamma
[
a
,
z
]
is the incomplete gamma function
.
Gamma
[
a
,
z
0
,
z
1
]
is the generalized incomplete gamma function
.
MORE INFORMATION
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
CLOSE ALL
Basic Examples
(4)
Integer values:
In[1]:=
Out[1]=
Half-integer values:
In[1]:=
Out[1]=
Evaluate numerically for complex arguments:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Scope
(5)
Generalizations & Extensions
(11)
Applications
(5)
Properties & Relations
(6)
Possible Issues
(2)
Neat Examples
(2)
SEE ALSO
Factorial
LogGamma
GammaRegularized
InverseGammaRegularized
PolyGamma
RiemannSiegelTheta
GammaDistribution
TUTORIALS
Special Functions
RELATED LINKS
Implementation notes: Numerical and Related Functions
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Functions Used in Statistics
Gamma Functions and Related Functions
Mathematical Functions
Special Functions
New in 1
© 2008 Wolfram Research, Inc.
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. 
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to 
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EXAMPLES
Basic Examples 
Scope 