Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aa78)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.aa78.01

Input Form

HypergeometricPFQ[{-(3/2), 5}, {-(11/2), -(11/2)}, -z] == (1/108056025) (108056025 + 26790750 z + 1984500 z^2 - 189000 z^3 + 90720 z^4 - 181440 z^5 + 4233600 z^6 - 80680320 z^7 + 152570880 z^8 - 94797696 z^9 + 26302464 z^10 - 3671280 z^11 + 265504 z^12 - 9408 z^13 + 128 z^14) - (1/108056025) ((8 Sqrt[Pi] (2441880 z^(13/2) - 16279200 z^(15/2) + 23796360 z^(17/2) - 13300560 z^(19/2) + 3502065 z^(21/2) - 474936 z^(23/2) + 33768 z^(25/2) - 1184 z^(27/2) + 16 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]