Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ai3l)

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=2, a₂>=2

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

For fixed z and a₁=2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ai3l.01

Input Form

HypergeometricPFQ[{2, 9/2}, {-(9/2), -(9/2)}, z] == (1/93767625) (93767625 + 41674500 z + 28066500 z^2 + 38918880 z^3 + 162162000 z^4 + 6616209600 z^5 + 216028088640 z^6 + 698315627520 z^7 + 748293251328 z^8 + 368645575680 z^9 + 96392340480 z^10 + 14323064832 z^11 + 1237241856 z^12 + 60932096 z^13 + 1572864 z^14 + 16384 z^15) + (1/93767625) (8192 E^z Sqrt[Pi] (4717440 z^(11/2) + 49714560 z^(13/2) + 117573120 z^(15/2) + 109589760 z^(17/2) + 50168160 z^(19/2) + 12573792 z^(21/2) + 1820448 z^(23/2) + 154656 z^(25/2) + 7533 z^(27/2) + 193 z^(29/2) + 2 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]