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

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, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5, 6}, {-(7/2), 2}, -z] == (1/2419200) (2419200 + 10368000 z + 29030400 z^2 + 90316800 z^3 + 650280960 z^4 - 1604937735 z^5 + 1169641050 z^6 - 393076980 z^7 + 70228440 z^8 - 7021648 z^9 + 390624 z^10 - 11200 z^11 + 128 z^12) + (1/4838400) ((Sqrt[Pi] (-2296748025 z^(9/2) + 4111660800 z^(11/2) - 2676533040 z^(13/2) + 850239360 z^(15/2) - 147114720 z^(17/2) + 14423040 z^(19/2) - 792320 z^(21/2) + 22528 z^(23/2) - 256 z^(25/2)) Erfi[Sqrt[z]])/E^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]