Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9418)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.9418.01

Input Form

HypergeometricPFQ[{-(19/4)}, {1/2, 9/4}, z] == (1/(750822359040 z^(5/4))) ((4 z^(1/4) (1964187225 + 2618916300 Sqrt[z] + 33093936720 z - 190758231360 z^(3/2) - 28732147200 z^2 + 124998727680 z^(5/2) + 3754598400 z^3 - 15385657344 z^(7/2) - 126025728 z^4 + 507248640 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (1964187225 - 2618916300 Sqrt[z] + 33093936720 z + 190758231360 z^(3/2) - 28732147200 z^2 - 124998727680 z^(5/2) + 3754598400 z^3 + 15385657344 z^(7/2) - 126025728 z^4 - 507248640 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (1964187225 - 62853991200 z + 838053216000 z^2 - 510813388800 z^3 + 61916774400 z^4 - 2032140288 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (1964187225 - 62853991200 z + 838053216000 z^2 - 510813388800 z^3 + 61916774400 z^4 - 2032140288 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 838053216000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 62853991200 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1964187225 </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 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep 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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]