Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ahb8)

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=-9/2

http://functions.wolfram.com/07.25.03.ahb8.01

Input Form

HypergeometricPFQ[{3/2, 6}, {-(9/2), -(9/2)}, -z] == (1/13395375) (13395375 - 5953500 z + 4252500 z^2 - 6350400 z^3 + 28576800 z^4 - 1257379200 z^5 + 44697744000 z^6 - 158856768000 z^7 + 189245185920 z^8 - 105202045440 z^9 + 31670886240 z^10 - 5571720000 z^11 + 593535600 z^12 - 38452992 z^13 + 1469184 z^14 - 30208 z^15 + 256 z^16) - (1/13395375) ((8 Sqrt[Pi] (-952333200 z^(11/2) + 10841947200 z^(13/2) - 27996154200 z^(15/2) + 28864458000 z^(17/2) - 14855560650 z^(19/2) + 4275235440 z^(21/2) - 731370465 z^(23/2) + 76508010 z^(25/2) - 4896600 z^(27/2) + 185520 z^(29/2) - 3792 z^(31/2) + 32 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]