Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an3o)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-5/2

http://functions.wolfram.com/07.25.03.an3o.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(5/2), 11/2}, -z] == (1/(800 z^4)) (-529200 - 176400 z - 52920 z^2 - 12600 z^3 - 1650 z^4 + 1170 z^5 + 3045 z^6 + 14329 z^7 - 15900 z^8 + 4600 z^9 - 480 z^10 + 16 z^11) + (1/(1600 z^(9/2))) ((Sqrt[Pi] (529200 + 529200 z + 264600 z^2 + 88200 z^3 + 22050 z^4 + 4410 z^5 + 735 z^6 + 105 z^7 - 41010 z^8 + 35960 z^9 - 9664 z^10 + 976 z^11 - 32 z^12) 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]