Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8964)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8964.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(13/4)}, z] == (1/(3163404404160 z^(5/2))) ((-948702429675 + 948702429675 E^(4 Sqrt[z]) - 1897404859350 Sqrt[z] - 1897404859350 E^(4 Sqrt[z]) Sqrt[z] - 1044947603700 z + 1044947603700 E^(4 Sqrt[z]) z + 439977938400 z^(3/2) + 439977938400 E^(4 Sqrt[z]) z^(3/2) - 138940401600 z^2 + 138940401600 E^(4 Sqrt[z]) z^2 + 42551308800 z^(5/2) + 42551308800 E^(4 Sqrt[z]) z^(5/2) - 13699445760 z^3 + 13699445760 E^(4 Sqrt[z]) z^3 + 4853882880 z^(7/2) + 4853882880 E^(4 Sqrt[z]) z^(7/2) - 1966325760 z^4 + 1966325760 E^(4 Sqrt[z]) z^4 + 949616640 z^(9/2) + 949616640 E^(4 Sqrt[z]) z^(9/2) - 578027520 z^5 + 578027520 E^(4 Sqrt[z]) z^5 + 484442112 z^(11/2) + 484442112 E^(4 Sqrt[z]) z^(11/2) - 666894336 z^6 + 666894336 E^(4 Sqrt[z]) z^6 + 2717908992 z^(13/2) + 2717908992 E^(4 Sqrt[z]) z^(13/2) + 16777216 z^7 - 16777216 E^(4 Sqrt[z]) z^7 - 67108864 z^(15/2) - 67108864 E^(4 Sqrt[z]) z^(15/2) - 4194304 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (-651 + 16 z) Erf[Sqrt[2] z^(1/4)] + 4194304 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (-651 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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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'> 16 </cn> <ci> z </ci> </apply> <cn type='integer'> -651 </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> <power /> <ci> z </ci> <cn type='rational'> 27 <sep /> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2717908992 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2717908992 </cn> <apply> 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type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 578027520 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 578027520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 949616640 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 949616640 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> 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<cn type='integer'> 13699445760 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13699445760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 42551308800 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 42551308800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 138940401600 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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]