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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(9/2), -(7/2)}, -z] == (1/281302875) (281302875 - 392931000 z + 729729000 z^2 - 2918916000 z^3 + 57891834000 z^4 + 3519823507200 z^5 - 49279934995200 z^6 + 133997460710400 z^7 - 145123982035200 z^8 + 79835752396800 z^9 - 25148703098880 z^10 + 4845395681280 z^11 - 591323443200 z^12 + 46268989440 z^13 - 2297794560 z^14 + 69556224 z^15 - 1163264 z^16 + 8192 z^17) - (1/281302875) ((1024 Sqrt[Pi] (12029472000 z^(11/2) - 84668976000 z^(13/2) + 180071942400 z^(15/2) - 172431504000 z^(17/2) + 88432948800 z^(19/2) - 26683927200 z^(21/2) + 5000486400 z^(23/2) - 599014440 z^(25/2) + 46273950 z^(27/2) - 2277345 z^(29/2) + 68490 z^(31/2) - 1140 z^(33/2) + 8 z^(35/2)) 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]