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

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

For fixed z and a₁=11/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), 23/4}, z] == (1/(270582939648 z^(19/4))) ((19 (4 z^(1/4) (-26264240610733125 - 35018987480977500 Sqrt[z] - 26648595351378000 z - 14186553813432000 z^(3/2) - 5684129753702400 z^2 - 1790105193676800 z^(5/2) - 454523269939200 z^3 - 94039297228800 z^(7/2) - 15804923904000 z^4 - 2114281537536 z^(9/2) - 214614147072 z^5 - 14898167808 z^(11/2) - 536870912 z^6 + E^(4 Sqrt[z]) (26264240610733125 - 35018987480977500 Sqrt[z] + 26648595351378000 z - 14186553813432000 z^(3/2) + 5684129753702400 z^2 - 1790105193676800 z^(5/2) + 454523269939200 z^3 - 94039297228800 z^(7/2) + 15804923904000 z^4 - 2114281537536 z^(9/2) + 214614147072 z^5 - 14898167808 z^(11/2) + 536870912 z^6)) + 104928949125 E^(2 Sqrt[z]) Sqrt[2 Pi] (250305 - 13024 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 104928949125 E^(2 Sqrt[z]) Sqrt[2 Pi] (250305 - 13024 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 26648595351378000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35018987480977500 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 26264240610733125 </cn> </apply> </apply> <cn type='integer'> -26264240610733125 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 104928949125 </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'> 256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> 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<cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13024 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 250305 </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> </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]