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

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=6, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{-(3/2), 6}, {-(11/2), -(1/2)}, -z] == (1/207900) (207900 + 680400 z + 551880 z^2 + 225960 z^3 + 35532 z^4 - 43380 z^5 - 192115 z^6 + 85752 z^7 - 12736 z^8 + 768 z^9 - 16 z^10) + (1/415800) ((Sqrt[Pi] (-1081080 z^(3/2) - 1081080 z^(5/2) - 540540 z^(7/2) - 180180 z^(9/2) - 45045 z^(11/2) + 459018 z^(13/2) - 183512 z^(15/2) + 26224 z^(17/2) - 1552 z^(19/2) + 32 z^(21/2)) 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]