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

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=-11/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(11/2), -(11/2)}, -z] == (1/102112943625) (102112943625 - 55697969250 z + 35756721000 z^2 - 36486450000 z^3 + 74432358000 z^4 - 439977938400 z^5 + 24638764550400 z^6 - 1123668537868800 z^7 + 5160888457401600 z^8 - 8018344440691200 z^9 + 5905552963368960 z^10 - 2410712344719360 z^11 + 594117835960320 z^12 - 92816606453760 z^13 + 9425873141760 z^14 - 625988272128 z^15 + 26800816128 z^16 - 708345856 z^17 + 10452992 z^18 - 65536 z^19) + (1/102112943625) ((16384 Sqrt[Pi] (-10178784000 z^(13/2) + 144538732800 z^(15/2) - 471517200000 z^(17/2) + 624159043200 z^(19/2) - 420972552000 z^(21/2) + 163010232000 z^(23/2) - 38848027680 z^(25/2) + 5935485600 z^(27/2) - 593646570 z^(29/2) + 39004350 z^(31/2) - 1657095 z^(33/2) + 43551 z^(35/2) - 640 z^(37/2) + 4 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]