Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad9s)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ad9s.01

Input Form

HypergeometricPFQ[{9/4}, {-(11/2), 17/4}, z] == (1/(9688842240 z^(13/4))) ((13 (4 z^(1/4) (1996138596375 + 2661518128500 Sqrt[z] + 2027823336000 z + 1081505779200 z^(3/2) + 432602311680 z^2 + 134837084160 z^(5/2) + 33130168320 z^3 + 6332743680 z^(7/2) + 900464640 z^4 + 85983232 z^(9/2) + 4194304 z^5 + E^(4 Sqrt[z]) (1996138596375 - 2661518128500 Sqrt[z] + 2027823336000 z - 1081505779200 z^(3/2) + 432602311680 z^2 - 134837084160 z^(5/2) + 33130168320 z^3 - 6332743680 z^(7/2) + 900464640 z^4 - 85983232 z^(9/2) + 4194304 z^5)) + 6336947925 E^(2 Sqrt[z]) Sqrt[2 Pi] (-315 + 16 z) Erf[Sqrt[2] z^(1/4)] + 6336947925 E^(2 Sqrt[z]) Sqrt[2 Pi] (-315 + 16 z) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2661518128500 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 1996138596375 </cn> </apply> </apply> <cn type='integer'> 1996138596375 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6336947925 </cn> <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'> 16 </cn> <ci> z </ci> </apply> <cn type='integer'> -315 </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 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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]