Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ug)

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.a7ug.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(9/4)}, z] == (1/(139050743040 z^(7/2))) ((225881530875 - 225881530875 E^(4 Sqrt[z]) + 451763061750 Sqrt[z] + 451763061750 E^(4 Sqrt[z]) Sqrt[z] + 329983453800 z - 329983453800 E^(4 Sqrt[z]) z + 57616158600 z^(3/2) + 57616158600 E^(4 Sqrt[z]) z^(3/2) - 35286451200 z^2 + 35286451200 E^(4 Sqrt[z]) z^2 + 13232419200 z^(5/2) + 13232419200 E^(4 Sqrt[z]) z^(5/2) - 4704860160 z^3 + 4704860160 E^(4 Sqrt[z]) z^3 + 1766983680 z^(7/2) + 1766983680 E^(4 Sqrt[z]) z^(7/2) - 743178240 z^4 + 743178240 E^(4 Sqrt[z]) z^4 + 368148480 z^(9/2) + 368148480 E^(4 Sqrt[z]) z^(9/2) - 228065280 z^5 + 228065280 E^(4 Sqrt[z]) z^5 + 193462272 z^(11/2) + 193462272 E^(4 Sqrt[z]) z^(11/2) - 268435456 z^6 + 268435456 E^(4 Sqrt[z]) z^6 + 1098907648 z^(13/2) + 1098907648 E^(4 Sqrt[z]) z^(13/2) + 8388608 z^7 - 8388608 E^(4 Sqrt[z]) z^7 - 33554432 z^(15/2) - 33554432 E^(4 Sqrt[z]) z^(15/2) - 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (-527 + 16 z) Erf[Sqrt[2] z^(1/4)] + 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (-527 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 228065280 </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'> 228065280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 368148480 </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'> 368148480 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> 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</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'> 4704860160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13232419200 </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'> 13232419200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35286451200 </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'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35286451200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 57616158600 </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'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 57616158600 </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'> 329983453800 </cn> 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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]