Hypergeometric2F1
Plotting
Evaluation
Hypergeometric Functions
Hypergeometric2F1[
a
,
b
,c,
z
] (111951 formulas)
Primary definition (8 formulas)
Specific values (111271 formulas)
General characteristics (24 formulas)
Series representations (71 formulas)
Integral representations (7 formulas)
Limit representations (3 formulas)
Continued fraction representations (2 formulas)
Differential equations (53 formulas)
Transformations (8 formulas)
Identities (151 formulas)
Differentiation (51 formulas)
Integration (15 formulas)
Integral transforms (1 formula)
Summation (3 formulas)
Operations (9 formulas)
Representations through more general functions (273 formulas)
Representations through equivalent functions (1 formula)
Theorems (0 formulas)
History (0 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
]