Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ago7)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=4, b₁>=-11/2

For fixed z and a₁=3/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.ago7.01

Input Form

HypergeometricPFQ[{3/2, 4}, {-(11/2), 11/2}, -z] == (1/(66 z^4)) (-63504000 - 18446400 z - 5382720 z^2 - 1217160 z^3 - 222246 z^4 - 33804 z^5 - 4380 z^6 - 491 z^7 - 48 z^8 - 4 z^9) + (1/(132 z^(9/2))) ((Sqrt[Pi] (63504000 + 60782400 z + 28969920 z^2 + 9160200 z^3 + 2159640 z^4 + 404460 z^5 + 62580 z^6 + 8211 z^7 + 930 z^8 + 92 z^9 + 8 z^10) 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]