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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 3}, {-(11/2), -(9/2)}, -z] == (1/29469825) (29469825 - 8930250 z + 3969000 z^2 - 3402000 z^3 + 7484400 z^4 - 90810720 z^5 - 3632428800 z^6 + 31872960000 z^7 - 54606263040 z^8 + 36624268800 z^9 - 12059117568 z^10 + 2155008000 z^11 - 217190400 z^12 + 12214272 z^13 - 354304 z^14 + 4096 z^15) - (1/29469825) ((1024 Sqrt[Pi] (-10281600 z^(13/2) + 48323520 z^(15/2) - 67193280 z^(17/2) + 40818960 z^(19/2) - 12736080 z^(21/2) + 2205000 z^(23/2) - 217896 z^(25/2) + 12099 z^(27/2) - 348 z^(29/2) + 4 z^(31/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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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]