Hypergeometric2F1
Hypergeometric Functions
Hypergeometric2F1[
a
,
b
,c,
z
]
Identities
Functional identities (130 formulas)
Relations between contiguous functions (26 formulas)
Additional relations between contiguous functions (2 formulas)
Relations for fixed z (3 formulas)
Relations of special kind (5 formulas)
Reduction to polynomial (6 formulas)
Division on even and odd parts and generalization (3 formulas)
Generic general cases (9 formulas)
Confluent general cases (3 formulas)
Relations including three Kummer's solutions (20 formulas)
Quadratic transformations with fixed
a
,
b
,
z
(29 formulas)
Quadratic transformations with fixed
a
,
c
,
z
(8 formulas)
Cubic transformations (16 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
]