Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7514)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-9/4

http://functions.wolfram.com/07.22.03.7514.01

Input Form

HypergeometricPFQ[{5}, {-(9/4), 1/4}, z] == (1/34560) ((-8 E^(2 Sqrt[z]) (-4320 - 27435 z + 44148 z^2 + 4672 z^3) - E^(4 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (65835 - 131670 Sqrt[z] - 12540 z + 200640 z^(3/2) + 109440 z^2 + 18944 z^(5/2) + 1024 z^3) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(3/4) (-65835 - 131670 Sqrt[z] + 12540 z + 200640 z^(3/2) - 109440 z^2 + 18944 z^(5/2) - 1024 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]