Hypergeometric2F1
Hypergeometric Functions
Hypergeometric2F1[
a
,
b
,c,
z
]
Representations through more general functions
Through Meijer
G
(266 formulas)
Classical cases for the direct function itself (9 formulas)
Classical cases involving algebraic functions with linear arguments (8 formulas)
Classical cases involving algebraic functions with rational arguments (7 formulas)
Classical cases involving algebraic functions with quadratic arguments (8 formulas)
Classical cases involving algebraic functions with squares in arguments (15 formulas)
Classical cases involving algebraic functions with cubics in arguments (8 formulas)
Classical cases with rational arguments and unit step theta (4 formulas)
Classical cases involving algebraic functions with linear arguments and unit step theta (4 formulas)
Classical cases involving algebraic functions with rational arguments and unit step theta (12 formulas)
Classical cases involving sgn (8 formulas)
Classical cases involving powers of
2
F
1
(10 formulas)
Classical cases for products of
2
F
1
with linear arguments (5 formulas)
Classical cases involving products of
2
F
1
with linear arguments (8 formulas)
Classical cases for products of
2
F
1
with algebraic arguments (10 formulas)
Classical cases involving products of
2
F
1
with algebraic arguments (20 formulas)
Classical cases involving
2
F
~
1
with linear arguments (11 formulas)
Classical cases involving algebraic functions and
2
F
~
1
with linear arguments (12 formulas)
Classical cases involving
2
F
~
1
with algebraic arguments (14 formulas)
Classical cases involving algebraic functions and
2
F
~
1
with algebraic arguments (34 formulas)
Generalized cases for the direct function itself (2 formulas)
Generalized cases involving algebraic functions with quadratic arguments (4 formulas)
Generalized cases involving algebraic functions with squares in arguments (8 formulas)
Classical cases involving sgn (3 formulas)
Generalized cases involving powers of
2
F
1
(3 formulas)
Generalized cases for products of
2
F
1
with algebraic arguments (5 formulas)
Generalized cases involving products of
2
F
1
with algebraic arguments (10 formulas)
Generalized cases involving
2
F
~
1
with algebraic arguments (7 formulas)
Generalized cases involving algebraic functions and
2
F
~
1
with algebraic arguments (17 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
]
