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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-11/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(11/2), -(5/2)}, -z] == (1/7016625) (7016625 - 8930250 z + 17860500 z^2 - 130977000 z^3 - 1362160800 z^4 - 8172964800 z^5 - 92626934400 z^6 + 396338054400 z^7 - 465324652800 z^8 + 249089379840 z^9 - 72222151680 z^10 + 12293798400 z^11 - 1273672320 z^12 + 80629440 z^13 - 3022464 z^14 + 61184 z^15 - 512 z^16) + (1/7016625) ((32 Sqrt[Pi] (6153537600 z^(13/2) - 17435023200 z^(15/2) + 17646174000 z^(17/2) - 8760376800 z^(19/2) + 2431884600 z^(21/2) - 402932070 z^(23/2) + 41017185 z^(25/2) - 2565960 z^(27/2) + 95400 z^(29/2) - 1920 z^(31/2) + 16 z^(33/2)) 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]