Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8146)

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/07.22.03.8146.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), -(15/4)}, z] == (1/12162150) ((6081075 + 6081075 E^(4 Sqrt[z]) + 12162150 Sqrt[z] - 12162150 E^(4 Sqrt[z]) Sqrt[z] + 5945940 z + 5945940 E^(4 Sqrt[z]) z - 4324320 z^(3/2) + 4324320 E^(4 Sqrt[z]) z^(3/2) + 2358720 z^2 + 2358720 E^(4 Sqrt[z]) z^2 - 1344000 z^(5/2) + 1344000 E^(4 Sqrt[z]) z^(5/2) + 906240 z^3 + 906240 E^(4 Sqrt[z]) z^3 - 811008 z^(7/2) + 811008 E^(4 Sqrt[z]) z^(7/2) + 1163264 z^4 + 1163264 E^(4 Sqrt[z]) z^4 - 4849664 z^(9/2) + 4849664 E^(4 Sqrt[z]) z^(9/2) - 65536 z^5 - 65536 E^(4 Sqrt[z]) z^5 + 262144 z^(11/2) - 262144 E^(4 Sqrt[z]) z^(11/2) + 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-299 + 16 z) Erf[Sqrt[2] z^(1/4)] + 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-299 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</cn> <apply> <times /> <cn type='integer'> 4324320 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5945940 </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> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 5945940 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12162150 </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'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 12162150 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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]