Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7v8)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7v8.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 19/4}, z] == (4 z^(1/4) (-241886151295425 - 2424817473705900 Sqrt[z] + 271552488938640 z - 3013261759609920 z^(3/2) + 177676424190720 z^2 - 2530170073267200 z^(5/2) - 929077290086400 z^3 + 4074690368028672 z^(7/2) + 135686522732544 z^4 - 558143268716544 z^(9/2) - 5365627355136 z^5 + 21671184433152 z^(11/2) + 70481084416 z^6 - 282729644032 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (241886151295425 - 2424817473705900 Sqrt[z] - 271552488938640 z - 3013261759609920 z^(3/2) - 177676424190720 z^2 - 2530170073267200 z^(5/2) + 929077290086400 z^3 + 4074690368028672 z^(7/2) - 135686522732544 z^4 - 558143268716544 z^(9/2) + 5365627355136 z^5 + 21671184433152 z^(11/2) - 70481084416 z^6 - 282729644032 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-2911567756672575 - 11293353722851200 z - 12906689968972800 z^2 - 12515578151731200 z^3 + 16687437535641600 z^4 - 2248412636381184 z^5 + 86895174352896 z^6 - 1131723882496 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-2911567756672575 - 11293353722851200 z - 12906689968972800 z^2 - 12515578151731200 z^3 + 16687437535641600 z^4 - 2248412636381184 z^5 + 86895174352896 z^6 - 1131723882496 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(75406362858749952 z^(15/4))

Standard Form

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MathML Form

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<power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </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 /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4294967296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1131723882496 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 86895174352896 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> 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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]