Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aiu4)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-9/2

http://functions.wolfram.com/07.25.03.aiu4.01

Input Form

HypergeometricPFQ[{5/2, 3}, {-(9/2), -(7/2)}, z] == (1/297675) (297675 + 141750 z + 113400 z^2 + 226800 z^3 + 2494800 z^4 - 90810720 z^5 - 707616000 z^6 - 1064286720 z^7 - 614949120 z^8 - 169751040 z^9 - 24425472 z^10 - 1858560 z^11 - 70144 z^12 - 1024 z^13) - (1/297675) (256 E^z Sqrt[Pi] (982800 z^(11/2) + 4158000 z^(13/2) + 5118120 z^(15/2) + 2693880 z^(17/2) + 707490 z^(19/2) + 98910 z^(21/2) + 7395 z^(23/2) + 276 z^(25/2) + 4 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]