Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8go)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a8go.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(7/2), 23/4}, z] == (209 (4 z^(1/4) (-10128266814290625 - 13504355752387500 Sqrt[z] - 8184458031750000 z - 2681384345640000 z^(3/2) - 409880199456000 z^2 - 14387248512000 z^(5/2) - 3845153894400 z^3 + 7989707980800 z^(7/2) - 1441951580160 z^4 + 5156858757120 z^(9/2) - 163750871040 z^5 + 625307811840 z^(11/2) - 8975810560 z^6 + 35097935872 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (10128266814290625 - 13504355752387500 Sqrt[z] + 8184458031750000 z - 2681384345640000 z^(3/2) + 409880199456000 z^2 - 14387248512000 z^(5/2) + 3845153894400 z^3 + 7989707980800 z^(7/2) + 1441951580160 z^4 + 5156858757120 z^(9/2) + 163750871040 z^5 + 625307811840 z^(11/2) + 8975810560 z^6 + 35097935872 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (10128266814290625 - 2619026570160000 z + 459766419840000 z^2 - 84071573913600 z^3 + 26689388544000 z^4 + 20095539609600 z^5 + 2473297182720 z^6 + 139586437120 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (10128266814290625 - 2619026570160000 z + 459766419840000 z^2 - 84071573913600 z^3 + 26689388544000 z^4 + 20095539609600 z^5 + 2473297182720 z^6 + 139586437120 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(29554872554618880 z^(19/4))

Standard Form

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MathML Form

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type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14387248512000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 409880199456000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2681384345640000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8184458031750000 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13504355752387500 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 10128266814290625 </cn> </apply> </apply> <cn type='integer'> -10128266814290625 </cn> </apply> </apply> 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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]