Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alyt)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.alyt.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(11/2), -(11/2)}, -z] == (1/34037647875) (34037647875 - 20253807000 z + 13752585000 z^2 - 14594580000 z^3 + 30648618000 z^4 - 185253868800 z^5 + 10559470521600 z^6 - 489540288384000 z^7 + 2282555730067200 z^8 - 3595884955084800 z^9 + 2682958648965120 z^10 - 1108735057059840 z^11 + 276465163161600 z^12 - 43679434014720 z^13 + 4484193976320 z^14 - 300947521536 z^15 + 13016727552 z^16 - 347463680 z^17 + 5177344 z^18 - 32768 z^19) + (1/34037647875) ((4096 Sqrt[Pi] (-17581536000 z^(13/2) + 253174118400 z^(15/2) - 836984534400 z^(17/2) + 1122144710400 z^(19/2) - 766162152000 z^(21/2) + 300192480000 z^(23/2) - 72359814240 z^(25/2) + 11178181440 z^(27/2) - 1130022090 z^(29/2) + 75021600 z^(31/2) - 3219705 z^(33/2) + 85458 z^(35/2) - 1268 z^(37/2) + 8 z^(39/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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<apply> <ci> Erfi </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]