Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am0e)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.am0e.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(7/2), -(7/2)}, z] == (1/3472875) (3472875 + 5103000 z + 11226600 z^2 + 64864800 z^3 + 3405402000 z^4 + 140972832000 z^5 + 572125881600 z^6 + 766297082880 z^7 + 473618384640 z^8 + 157191628800 z^9 + 30284789760 z^10 + 3513753600 z^11 + 246796288 z^12 + 10182144 z^13 + 225280 z^14 + 2048 z^15) + (1/3472875) (256 E^z Sqrt[Pi] (86486400 z^(9/2) + 1116460800 z^(11/2) + 3235680000 z^(13/2) + 3712665600 z^(15/2) + 2111407200 z^(17/2) + 667356480 z^(19/2) + 124726560 z^(21/2) + 14188800 z^(23/2) + 983505 z^(25/2) + 40210 z^(27/2) + 884 z^(29/2) + 8 z^(31/2)) Erf[Sqrt[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]