Hypergeometric1F1
Hypergeometric Functions
Hypergeometric1F1[
a
,
b
,
z
]
Representations through more general functions
Through Meijer
G
(67 formulas)
Classical cases for the direct function itself (12 formulas)
Classical cases involving exp (1 formula)
Classical cases involving exp and cosh (1 formula)
Classical cases involving exp and sinh (1 formula)
Classical cases for products of
_{1}
F
_{1}
(4 formulas)
Classical cases involving exp and products of
_{1}
F
_{1}
(4 formulas)
Classical cases involving
_{1}
F
^{~}
_{1}
(4 formulas)
Classical cases involving exp and
_{1}
F
^{~}
_{1}
(4 formulas)
Classical cases involving hypergeometric
U
(2 formulas)
Classical cases involving exp and hypergeometric
U
(2 formulas)
Classical cases involving Laguerre
L
(4 formulas)
Classical cases involving exp and Laguerre
L
(2 formulas)
Generalized cases for the direct function itself (2 formulas)
Generalized cases for products of
_{1}
F
_{1}
(4 formulas)
Generalized cases involving exp and products of
_{1}
F
_{1}
(4 formulas)
Generalized cases involving
_{1}
F
^{~}
_{1}
(4 formulas)
Generalized cases involving exp and
_{1}
F
^{~}
_{1}
(4 formulas)
Generalized cases involving hypergeometric
U
(1 formula)
Generalized cases involving exp and hypergeometric
U
(1 formula)
Generalized cases involving Laguerre
L
(4 formulas)
Generalized cases involving exp and Laguerre
L
(2 formulas)
HypergeometricPFQ[{},{},
z
]
HypergeometricPFQ[{},{
b
},
z
]
HypergeometricPFQ[{
a
},{},
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
]
HypergeometricPFQ[{
a
_{1}
,...,
a
_{p}
},{
b
_{1}
,...,
b
_{q}
},
z
]