Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8346)

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`=5/2

http://functions.wolfram.com/07.22.03.8346.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(7/4)}, z] == (1/(50874642000 z^(3/2))) ((2657429775 - 2657429775 E^(4 Sqrt[z]) + 5314859550 Sqrt[z] + 5314859550 E^(4 Sqrt[z]) Sqrt[z] - 6541365600 z + 6541365600 E^(4 Sqrt[z]) z + 5268110400 z^(3/2) + 5268110400 E^(4 Sqrt[z]) z^(3/2) - 4000147200 z^2 + 4000147200 E^(4 Sqrt[z]) z^2 + 3338979840 z^(5/2) + 3338979840 E^(4 Sqrt[z]) z^(5/2) - 3493969920 z^3 + 3493969920 E^(4 Sqrt[z]) z^3 + 5587107840 z^(7/2) + 5587107840 E^(4 Sqrt[z]) z^(7/2) - 24869928960 z^4 + 24869928960 E^(4 Sqrt[z]) z^4 - 943518720 z^(9/2) - 943518720 E^(4 Sqrt[z]) z^(9/2) + 3868987392 z^5 - 3868987392 E^(4 Sqrt[z]) z^5 + 32538624 z^(11/2) + 32538624 E^(4 Sqrt[z]) z^(11/2) - 130940928 z^6 + 130940928 E^(4 Sqrt[z]) z^6 - 262144 z^(13/2) - 262144 E^(4 Sqrt[z]) z^(13/2) + 1048576 z^7 - 1048576 E^(4 Sqrt[z]) z^7 + 256 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (-99799875 + 15207600 z - 512256 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 256 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (-99799875 + 15207600 z - 512256 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3868987392 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 943518720 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 943518720 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </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'> 4096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 512256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15207600 </cn> <ci> z </ci> </apply> <cn type='integer'> -99799875 </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> <power /> <ci> z </ci> 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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]