Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ane1)

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=5, a₂>=5

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

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

http://functions.wolfram.com/07.25.03.ane1.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(5/2), -(5/2)}, -z] == (1/637875) (637875 - 2806650 z + 24324300 z^2 - 1702701000 z^3 + 90875584800 z^4 - 464821156800 z^5 + 774051707520 z^6 - 592423683840 z^7 + 244405612800 z^8 - 59211394560 z^9 + 8822661120 z^10 - 824236032 z^11 + 48018144 z^12 - 1680960 z^13 + 32128 z^14 - 256 z^15) + (1/637875) ((16 Sqrt[Pi] (778377600 z^(7/2) - 12454041600 z^(9/2) + 44296761600 z^(11/2) - 62161344000 z^(13/2) + 43319253600 z^(15/2) - 16902587520 z^(17/2) + 3953970720 z^(19/2) - 575795520 z^(21/2) + 52965225 z^(23/2) - 3052680 z^(25/2) + 106056 z^(27/2) - 2016 z^(29/2) + 16 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]