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

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=9/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{3, 9/2}, {-(11/2), -(1/2)}, -z] == (1/1091475) (1091475 - 5358150 z - 26195400 z^2 - 54054000 z^3 - 97297200 z^4 - 220540320 z^5 - 1241560320 z^6 + 2146798080 z^7 - 1133717760 z^8 + 275591680 z^9 - 34799616 z^10 + 2335744 z^11 - 78336 z^12 + 1024 z^13) - (1/1091475) ((256 Sqrt[Pi] (-7711200 z^(13/2) + 10195920 z^(15/2) - 4908960 z^(17/2) + 1140300 z^(19/2) - 140350 z^(21/2) + 9275 z^(23/2) - 308 z^(25/2) + 4 z^(27/2)) 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]