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
=-3/2,
a
2
>=-3/2 (6307 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=-3/2,
a
3
>=-3/2 (1122 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=-1/2,
a
3
>=-1/2 (1014 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=1/2,
a
3
>=1/2 (898 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=1,
a
3
>=1 (844 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=3/2,
a
3
>=3/2 (667 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=2,
a
3
>=2 (608 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=5/2,
a
3
>=5/2 (437 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=3,
a
3
>=3 (370 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=7/2,
a
3
>=7/2 (213 formulas)
For fixed
z
and
a
1
=-3/2,
a
2
=4,
a
3
>=4 (134 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
},
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
]
