HypergeometricPFQ
Hypergeometric Functions
HypergeometricPFQ[{
a
1
,
a
2
,
a
3
},{
b
1
,
b
2
},
z
]
Specific values
For integer and half-integer parameters and fixed
z
For fixed
z
and
a
1
=1,
a
2
>=1
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
>=1
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3 (74 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=-7/2 (8 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=-5/2 (8 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=-3/2 (8 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=-1/2 (8 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=1/2 (8 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=1 (10 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=3/2 (6 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=2 (7 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=5/2 (4 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=3 (4 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=7/2 (2 formulas)
For fixed
z
and
a
1
=1,
a
2
=1,
a
3
=3,
b
1
=4 (1 formula)
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
},
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
,
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
]
