HypergeometricPFQ
Hypergeometric Functions
HypergeometricPFQ[{
a
1
,...,
a
p
},{
b
1
,...,
b
q
},
z
]
Series representations
Generalized power series
Expansions at
z
==infinity for
p
==
q
+1 (12 formulas)
The general formulas (2 formulas)
Case of simple poles (4 formulas)
Case of poles of order
r
in the points
a
r
+
k
/;
r
∈ {2,3,4} &&
k
∈
N
(1 formula)
The major terms for expansions of function
q
+1
F
q
(
a
1
,...,
a
q
+1
;
b
1
,...,
b
q
;
z
) at
z
==infinity (5 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
},{
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
]
