Hypergeometric2F1
Hypergeometric Functions
Hypergeometric2F1[
a
,
b
,c,
z
]
Specific values
Values at other
z
(40 formulas)
Values at
z
==-1/2 (1 formula)
Values at
z
==-1/3 (2 formulas)
Values at
z
==-1/8 (3 formulas)
Values at
z
==1/9 (1 formula)
Values at
z
==1/4 (1 formula)
Values at
z
==1/3 (1 formula)
Values at
z
==8/9 (4 formulas)
Values at
z
==2 (6 formulas)
Values at
z
==4-32
1/2
/8 (2 formulas)
Values at
z
==1-2
1/2
/2 (2 formulas)
Values at
z
==2-2
1/2
/4 (1 formula)
Values at
z
==22
1/2
-2 (2 formulas)
Values at
z
==122
1/2
-16 (4 formulas)
Values at
z
==2-3
1/2
/4 (1 formula)
Values at
z
==
e
+-Pi
i
/3
(4 formulas)
Values at
z
including phi (5 formulas)
HypergeometricPFQ[{},{},
z
]
HypergeometricPFQ[{},{
b
},
z
]
HypergeometricPFQ[{
a
},{},
z
]
HypergeometricPFQ[{
a
},{
b
},
z
]
HypergeometricPFQ[{
a
1
},{
b
1
,
b
2
},
z
]
HypergeometricPFQ[{
a
1
,
a
2
},{
b
1
,
b
2
},
z
]
HypergeometricPFQ[{
a
1
,
a
2
},{
b
1
,
b
2
,
b
3
},
z
]
HypergeometricPFQ[{
a
1
,
a
2
,
a
3
},{
b
1
,
b
2
},
z
]
HypergeometricPFQ[{
a
1
,
a
2
,
a
3
,
a
4
},{
b
1
,
b
2
,
b
3
},
z
]
HypergeometricPFQ[{
a
1
,
a
2
,
a
3
,
a
4
,
a
5
},{
b
1
,
b
2
,
b
3
,
b
4
},
z
]
HypergeometricPFQ[{
a
1
,
a
2
,
a
3
,
a
4
,
a
5
,
a
6
},{
b
1
,
b
2
,
b
3
,
b
4
,
b
5
},
z
]
HypergeometricPFQ[{
a
1
,...,
a
p
},{
b
1
,...,
b
q
},
z
]
