Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8174)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.8174.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 13/4}, z] == (-4 z^(1/4) (15346656950625 + 20462209267500 Sqrt[z] - 9821860448400 z - 25568017675200 z^(3/2) + 4031514789120 z^2 - 47721736258560 z^(5/2) + 3259033989120 z^3 - 39910699745280 z^(7/2) - 12805270732800 z^4 + 55230524030976 z^(9/2) + 1464521981952 z^5 - 5974958014464 z^(11/2) - 39879442432 z^6 + 160323076096 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (15346656950625 - 20462209267500 Sqrt[z] - 9821860448400 z + 25568017675200 z^(3/2) + 4031514789120 z^2 + 47721736258560 z^(5/2) + 3259033989120 z^3 + 39910699745280 z^(7/2) - 12805270732800 z^4 - 55230524030976 z^(9/2) + 1464521981952 z^5 + 5974958014464 z^(11/2) - 39879442432 z^6 - 160323076096 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (15346656950625 - 26191627862400 z + 133339196390400 z^2 + 203183537356800 z^3 + 193508130816000 z^4 - 225173097676800 z^5 + 24018463752192 z^6 - 642097610752 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (15346656950625 - 26191627862400 z + 133339196390400 z^2 + 203183537356800 z^3 + 193508130816000 z^4 - 225173097676800 z^5 + 24018463752192 z^6 - 642097610752 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(844218771701760 z^(9/4))

Standard Form

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MathML Form

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type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 39910699745280 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3259033989120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 47721736258560 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4031514789120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 25568017675200 </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'> 9821860448400 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20462209267500 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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]