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

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.amat.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(9/2), -(1/2)}, -z] == (1/2679075) (2679075 - 26195400 z - 243243000 z^2 - 972972000 z^3 - 3859455600 z^4 - 33522128640 z^5 + 106340532480 z^6 - 97469568000 z^7 + 41319694080 z^8 - 9469163520 z^9 + 1254594048 z^10 - 98036736 z^11 + 4419840 z^12 - 105472 z^13 + 1024 z^14) - (1/2679075) ((128 Sqrt[Pi] (-501228000 z^(11/2) + 1110412800 z^(13/2) - 895270320 z^(15/2) + 355713120 z^(17/2) - 78535170 z^(19/2) + 10168200 z^(21/2) - 782775 z^(23/2) + 34938 z^(25/2) - 828 z^(27/2) + 8 z^(29/2)) 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]