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

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=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(7/2), -(1/2)}, z] == (1/297675) (297675 + 3742200 z - 48648600 z^2 + 324324000 z^3 - 3859455600 z^4 - 16916739840 z^5 - 19596245760 z^6 - 10035809280 z^7 - 2697857280 z^8 - 410557440 z^9 - 36265728 z^10 - 1825152 z^11 - 48128 z^12 - 512 z^13) - (1/297675) (64 E^z Sqrt[Pi] (129729600 z^(9/2) + 371498400 z^(11/2) + 369457200 z^(13/2) + 175271040 z^(15/2) + 45110520 z^(17/2) + 6684930 z^(19/2) + 580545 z^(21/2) + 28890 z^(23/2) + 756 z^(25/2) + 8 z^(27/2)) 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]