Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6312)

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=1, b₁>=-23/4

For fixed z and a₁=1, b₁=-15/4

http://functions.wolfram.com/07.22.03.6312.01

Input Form

HypergeometricPFQ[{1}, {-(15/4), 15/4}, z] == (1/(960 z^(11/4))) ((-48 E^(2 Sqrt[z]) z^(3/4) (15015 + 1980 z + 76 z^2) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-135135 + 270270 Sqrt[z] - 249480 z + 138600 z^(3/2) - 50400 z^2 + 12096 z^(5/2) - 1792 z^3 + 128 z^(7/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (135135 + 270270 Sqrt[z] + 249480 z + 138600 z^(3/2) + 50400 z^2 + 12096 z^(5/2) + 1792 z^3 + 128 z^(7/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12096 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 50400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 138600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 249480 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 270270 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -135135 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 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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]
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