Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7720)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-19/4

http://functions.wolfram.com/07.22.03.7720.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), 19/4}, z] == (1/(597688320 z^(15/4))) ((-16 E^(2 Sqrt[z]) z^(3/4) (13266878625 + 5067562500 z + 1005404400 z^2 + 133895040 z^3 - 10325760 z^4 - 2138112 z^5 + 65536 z^6) - E^(4 Sqrt[z]) Sqrt[2 Pi] (39800635875 - 79601271750 Sqrt[z] + 83432349000 z - 60729669000 z^(3/2) + 34670235600 z^2 - 16670253600 z^(5/2) + 7178371200 z^3 - 2940537600 z^(7/2) + 1053561600 z^4 - 200578560 z^(9/2) - 64296960 z^5 + 60702720 z^(11/2) - 17039360 z^6 + 655360 z^(13/2) + 524288 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (39800635875 + 79601271750 Sqrt[z] + 83432349000 z + 60729669000 z^(3/2) + 34670235600 z^2 + 16670253600 z^(5/2) + 7178371200 z^3 + 2940537600 z^(7/2) + 1053561600 z^4 + 200578560 z^(9/2) - 64296960 z^5 - 60702720 z^(11/2) - 17039360 z^6 - 655360 z^(13/2) + 524288 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 60729669000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 83432349000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 79601271750 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 39800635875 </cn> </apply> <apply> <ci> Erfi </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> </apply> </apply> </annotation-xml> </semantics> </math>

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]