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

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=3, a₂>=3

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

For fixed z and a₁=3, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(9/2), -(9/2)}, z] == (1/843908625) (843908625 + 687629250 z + 729729000 z^2 + 1459458000 z^3 + 8270262000 z^4 + 439977938400 z^5 + 18841974278400 z^6 + 80459546227200 z^7 + 115133416070400 z^8 + 77253250521600 z^9 + 28355443292160 z^10 + 6181201244160 z^11 + 836200673280 z^12 + 71449927680 z^13 + 3830661120 z^14 + 124059648 z^15 + 2203648 z^16 + 16384 z^17) + (1/843908625) (4096 E^z Sqrt[Pi] (707616000 z^(11/2) + 9471168000 z^(13/2) + 28854403200 z^(15/2) + 35308224000 z^(17/2) + 21759192000 z^(19/2) + 7593264000 z^(21/2) + 1603476000 z^(23/2) + 212440320 z^(25/2) + 17896950 z^(27/2) + 950100 z^(29/2) + 30555 z^(31/2) + 540 z^(33/2) + 4 z^(35/2)) Erf[Sqrt[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]