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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=9/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {9/2, 23/4}, z] == -((1/(25769803776 z^(19/4))) ((7 (4 z^(1/4) (1140591375 + 1520788500 Sqrt[z] - 420843600 z + 2286792000 z^(3/2) - 219548160 z^2 + 978094080 z^(5/2) - 56401920 z^3 + 323911680 z^(7/2) + 36372480 z^4 - 148635648 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (-1140591375 + 1520788500 Sqrt[z] + 420843600 z + 2286792000 z^(3/2) + 219548160 z^2 + 978094080 z^(5/2) + 56401920 z^3 + 323911680 z^(7/2) - 36372480 z^4 - 148635648 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1140591375 + 7299784800 z + 8848224000 z^2 + 3852288000 z^3 + 1400832000 z^4 - 597688320 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-1140591375 + 7299784800 z + 8848224000 z^2 + 3852288000 z^3 + 1400832000 z^4 - 597688320 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> </apply> <apply> <times /> <cn type='integer'> 7299784800 </cn> <ci> z </ci> </apply> <cn type='integer'> -1140591375 </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> <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'> 16777216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 597688320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1400832000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3852288000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8848224000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7299784800 </cn> <ci> z </ci> </apply> <cn type='integer'> -1140591375 </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> </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]