Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ac4n)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=5, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.ac4n.01

Input Form

HypergeometricPFQ[{-(1/2), 5}, {-(11/2), -(5/2)}, -z] == (1/467775) (467775 + 85050 z - 18900 z^2 + 37800 z^3 + 151200 z^4 + 423360 z^5 + 2540160 z^6 - 4405680 z^7 + 2113080 z^8 - 431820 z^9 + 42024 z^10 - 1904 z^11 + 32 z^12) - (1/467775) ((2 Sqrt[Pi] (2034900 z^(13/2) - 2645370 z^(15/2) + 1155105 z^(17/2) - 225960 z^(19/2) + 21480 z^(21/2) - 960 z^(23/2) + 16 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]