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

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=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-11/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(11/2), -(3/2)}, -z] == (1/1403325) (1403325 - 2976750 z + 17860500 z^2 + 130977000 z^3 + 454053600 z^4 + 1634592960 z^5 + 13232419200 z^6 - 38567750400 z^7 + 33053287680 z^8 - 13225605120 z^9 + 2879804928 z^10 - 364376160 z^11 + 27301920 z^12 - 1184192 z^13 + 27264 z^14 - 256 z^15) + (1/1403325) ((16 Sqrt[Pi] (-1538384400 z^(13/2) + 3179327760 z^(15/2) - 2411141040 z^(17/2) + 907033680 z^(19/2) - 190606365 z^(21/2) + 23591745 z^(23/2) - 1742544 z^(25/2) + 74856 z^(27/2) - 1712 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]