Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al2n)

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=4, b₁>=-11/2

For fixed z and a₁=7/2, a₂=4, b₁=-9/2

http://functions.wolfram.com/07.25.03.al2n.01

Input Form

HypergeometricPFQ[{7/2, 4}, {-(9/2), -(7/2)}, -z] == (1/4465125) (4465125 - 3969000 z + 5103000 z^2 - 14968800 z^3 + 227026800 z^4 + 10897286400 z^5 - 116819539200 z^6 + 243166694400 z^7 - 199212168960 z^8 + 81194895360 z^9 - 18373416960 z^10 + 2432102400 z^11 - 190955520 z^12 + 8674816 z^13 - 208896 z^14 + 2048 z^15) - (1/4465125) ((256 Sqrt[Pi] (133660800 z^(11/2) - 745416000 z^(13/2) + 1238932800 z^(15/2) - 909946800 z^(17/2) + 349095600 z^(19/2) - 76187160 z^(21/2) + 9857400 z^(23/2) - 762465 z^(25/2) + 34290 z^(27/2) - 820 z^(29/2) + 8 z^(31/2)) 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]