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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{2, 11/2}, {-(9/2), -(5/2)}, z] == (1/13395375) (13395375 + 13097700 z + 24324300 z^2 + 194594400 z^3 - 2756754000 z^4 + 41902660800 z^5 + 217419733440 z^6 + 274924661760 z^7 + 148447676160 z^8 + 41265607680 z^9 + 6415150080 z^10 + 574169088 z^11 + 29110272 z^12 + 770048 z^13 + 8192 z^14) + (1/13395375) (4096 E^z Sqrt[Pi] (23587200 z^(11/2) + 76204800 z^(13/2) + 81648000 z^(15/2) + 40642560 z^(17/2) + 10795680 z^(19/2) + 1632960 z^(21/2) + 143640 z^(23/2) + 7200 z^(25/2) + 189 z^(27/2) + 2 z^(29/2)) 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]