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DOCUMENTATION CENTER SEARCH
Mathematica
>
Mathematics and Algorithms
>
Mathematical Functions
>
Special Functions
>
Hypergeometric Functions
>
Built-in
Mathematica
Symbol
Special Functions
Tutorials »
|
AppellF1
Hypergeometric1F1
HypergeometricPFQ
Hypergeometric2F1Regularized
LegendreP
LegendreQ
Pochhammer
See Also »
|
Functions for Separable Coordinate Systems
Hypergeometric Functions
Mathematical Functions
Special Functions
More About »
Hypergeometric2F1
Hypergeometric2F1
[
a
,
b
,
c
,
z
]
is the hypergeometric function
.
MORE INFORMATION
Mathematical function, suitable for both symbolic and numerical manipulation.
The
function has the series expansion
.
For certain special arguments,
Hypergeometric2F1
automatically evaluates to exact values.
Hypergeometric2F1
can be evaluated to arbitrary numerical precision.
Hypergeometric2F1
automatically threads over lists.
Hypergeometric2F1
[
a
,
b
,
c
,
z
]
has a branch cut discontinuity in the complex
plane running from
to
.
FullSimplify
and
FunctionExpand
include transformation rules for
Hypergeometric2F1
.
EXAMPLES
CLOSE ALL
Basic Examples
(4)
Evaluate numerically:
In[1]:=
Out[1]=
Evaluate symbolically:
In[1]:=
Out[1]=
Plot
:
In[1]:=
Out[1]=
Expand
Hypergeometric2F1
in a Taylor series at the origin:
In[1]:=
Out[1]=
Scope
(8)
Generalizations & Extensions
(2)
Applications
(1)
Properties & Relations
(2)
Possible Issues
(2)
Neat Examples
(1)
SEE ALSO
AppellF1
Hypergeometric1F1
HypergeometricPFQ
Hypergeometric2F1Regularized
LegendreP
LegendreQ
Pochhammer
TUTORIALS
Special Functions
RELATED LINKS
MathWorld
The Wolfram Functions Site
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Functions for Separable Coordinate Systems
Hypergeometric Functions
Mathematical Functions
Special Functions
New in 1 | Last modified in 4
. 
function has the series expansion 
. 
plane running from 
to 
.
EXAMPLES
Basic Examples 
Scope 