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
=-1/2,
a
2
>=-1/2
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
>=-1/2 (1010 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=-1/2 (94 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=1/2 (102 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=1 (114 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=3/2 (109 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=2 (117 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=5/2 (115 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=3 (119 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=7/2 (120 formulas)
For fixed
z
and
a
1
=-1/2,
a
2
=-1/2,
a
3
=4 (120 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
]
