Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ac4t)

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.ac4t.01

Input Form

HypergeometricPFQ[{-(1/2), 5}, {-(11/2), 1/2}, -z] == (1/62370) (62370 + 56700 z + 25200 z^2 + 6300 z^3 - 180 z^4 - 2163 z^5 - 7245 z^6 + 2550 z^7 - 260 z^8 + 8 z^9) + (1/124740) ((Sqrt[Pi] (-113400 Sqrt[z] - 113400 z^(3/2) - 56700 z^(5/2) - 18900 z^(7/2) - 4725 z^(9/2) - 945 z^(11/2) + 16800 z^(13/2) - 5352 z^(15/2) + 528 z^(17/2) - 16 z^(19/2)) 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]