Hypergeometric2F1
Hypergeometric Functions
Hypergeometric2F1[
a
,
b
,c,
z
]
Specific values (111271 formulas)
Values at
z
==0 (1 formula)
Values at
z
=1 (2 formulas)
Values at
z
==-1 (18 formulas)
Values at
z
=1/2 (24 formulas)
Values at other
z
(40 formulas)
Specialized values (176 formulas)
For integer and half-integer parameters and fixed
z
(3846 formulas)
For rational parameters with denominators 3 and fixed
z
(4396 formulas)
For rational parameters with denominators 4 and fixed
z
(21914 formulas)
For rational parameters with denominators 5 and fixed
z
(21776 formulas)
For rational parameters with denominators 6 and fixed
z
(4 formulas)
For rational parameters with denominators 8 and fixed
z
and
a
<0 (37236 formulas)
For rational parameters with denominators 8 and fixed
z
and
a
>0 (21774 formulas)
Values at fixed points (64 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
]
