Hypergeometric2F1
Hypergeometric Functions
Hypergeometric2F1[
a
,
b
,c,
z
]
Specific values
For rational parameters with denominators 8 and fixed
z
and
a
>0
For fixed
z
and
a
=1/8,
b
>=
a
(1224 formulas)
For fixed
z
and
a
=1/8,
b
=1/8 (7 formulas)
For fixed
z
and
a
=1/8,
b
=1/4 (14 formulas)
For fixed
z
and
a
=1/8,
b
=3/8 (21 formulas)
For fixed
z
and
a
=1/8,
b
=1/2 (14 formulas)
For fixed
z
and
a
=1/8,
b
=5/8 (56 formulas)
For fixed
z
and
a
=1/8,
b
=3/4 (14 formulas)
For fixed
z
and
a
=1/8,
b
=7/8 (38 formulas)
For fixed
z
and
a
=1/8,
b
=1 (25 formulas)
For fixed
z
and
a
=1/8,
b
=9/8 (8 formulas)
For fixed
z
and
a
=1/8,
b
=5/4 (15 formulas)
For fixed
z
and
a
=1/8,
b
=11/8 (21 formulas)
For fixed
z
and
a
=1/8,
b
=3/2 (15 formulas)
For fixed
z
and
a
=1/8,
b
=13/8 (57 formulas)
For fixed
z
and
a
=1/8,
b
=7/4 (15 formulas)
For fixed
z
and
a
=1/8,
b
=15/8 (39 formulas)
For fixed
z
and
a
=1/8,
b
=2 (23 formulas)
For fixed
z
and
a
=1/8,
b
=17/8 (9 formulas)
For fixed
z
and
a
=1/8,
b
=9/4 (16 formulas)
For fixed
z
and
a
=1/8,
b
=19/8 (22 formulas)
For fixed
z
and
a
=1/8,
b
=5/2 (16 formulas)
For fixed
z
and
a
=1/8,
b
=21/8 (58 formulas)
For fixed
z
and
a
=1/8,
b
=11/4 (16 formulas)
For fixed
z
and
a
=1/8,
b
=23/8 (40 formulas)
For fixed
z
and
a
=1/8,
b
=3 (23 formulas)
For fixed
z
and
a
=1/8,
b
=25/8 (10 formulas)
For fixed
z
and
a
=1/8,
b
=13/4 (17 formulas)
For fixed
z
and
a
=1/8,
b
=27/8 (23 formulas)
For fixed
z
and
a
=1/8,
b
=7/2 (17 formulas)
For fixed
z
and
a
=1/8,
b
=29/8 (59 formulas)
For fixed
z
and
a
=1/8,
b
=15/4 (17 formulas)
For fixed
z
and
a
=1/8,
b
=31/8 (41 formulas)
For fixed
z
and
a
=1/8,
b
=4 (23 formulas)
For fixed
z
and
a
=1/8,
b
=33/8 (11 formulas)
For fixed
z
and
a
=1/8,
b
=17/4 (18 formulas)
For fixed
z
and
a
=1/8,
b
=35/8 (24 formulas)
For fixed
z
and
a
=1/8,
b
=9/2 (18 formulas)
For fixed
z
and
a
=1/8,
b
=37/8 (60 formulas)
For fixed
z
and
a
=1/8,
b
=19/4 (18 formulas)
For fixed
z
and
a
=1/8,
b
=39/8 (42 formulas)
For fixed
z
and
a
=1/8,
b
=5 (23 formulas)
For fixed
z
and
a
=1/8,
b
=41/8 (12 formulas)
For fixed
z
and
a
=1/8,
b
=21/4 (19 formulas)
For fixed
z
and
a
=1/8,
b
=43/8 (25 formulas)
For fixed
z
and
a
=1/8,
b
=11/2 (19 formulas)
For fixed
z
and
a
=1/8,
b
=45/8 (61 formulas)
For fixed
z
and
a
=1/8,
b
=23/4 (19 formulas)
For fixed
z
and
a
=1/8,
b
=47/8 (43 formulas)
For fixed
z
and
a
=1/8,
b
=6 (23 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
]
