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

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=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(11/2), -(3/2)}, -z] == (1/467775) (467775 - 510300 z + 1984500 z^2 + 10584000 z^3 + 28576800 z^4 + 83825280 z^5 + 570810240 z^6 - 1296059400 z^7 + 874333800 z^8 - 272939940 z^9 + 45432828 z^10 - 4243776 z^11 + 221120 z^12 - 5952 z^13 + 64 z^14) - (1/467775) ((2 Sqrt[Pi] (491428350 z^(13/2) - 819047250 z^(15/2) + 496246275 z^(17/2) - 146892375 z^(19/2) + 23725650 z^(21/2) - 2175720 z^(23/2) + 112032 z^(25/2) - 2992 z^(27/2) + 32 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]