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New in 6.0: Mathematical Functions
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PolyGamma
PolyGamma
[
z
]
gives the digamma function
).
PolyGamma
[
n
,
z
]
gives the
derivative of the digamma function
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
PolyGamma
[
z
]
is the logarithmic derivative of the gamma function, given by
.
PolyGamma
[
n
,
z
]
is given for positive integer
by
.
For arbitrary complex
n
the polygamma function is defined by fractional calculus analytic continuation.
PolyGamma
[
z
]
and
PolyGamma
[
n
,
z
]
are meromorphic functions of
z
with no branch cut discontinuities.
For certain special arguments,
PolyGamma
automatically evaluates to exact values.
PolyGamma
can be evaluated to arbitrary numerical precision.
PolyGamma
automatically threads over lists.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Evaluate the digamma function:
In[1]:=
Out[1]=
Evaluate quadro-gamma:
In[2]:=
Out[2]=
Derivative of the gamma function:
In[1]:=
Out[1]=
The digamma function:
In[1]:=
Out[1]=
Scope
(9)
Generalizations & Extensions
(8)
Applications
(3)
Properties & Relations
(7)
Possible Issues
(3)
SEE ALSO
Gamma
LogGamma
EulerGamma
HarmonicNumber
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
Gamma Functions and Related Functions
Recurrence and Sum Functions
Special Functions
New in 6.0: Mathematical Functions
New in 1 | Last modified in 6
© 2008 Wolfram Research, Inc.
. 
by 
.
EXAMPLES
Basic Examples 
Scope 