Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8198)

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`=-1/2

http://functions.wolfram.com/07.22.03.8198.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), -(11/4)}, z] == (1/4594590) ((2297295 + 2297295 E^(4 Sqrt[z]) + 4594590 Sqrt[z] - 4594590 E^(4 Sqrt[z]) Sqrt[z] - 5012280 z - 5012280 E^(4 Sqrt[z]) z + 4038720 z^(3/2) - 4038720 E^(4 Sqrt[z]) z^(3/2) - 3379200 z^2 - 3379200 E^(4 Sqrt[z]) z^2 + 3488256 z^(5/2) - 3488256 E^(4 Sqrt[z]) z^(5/2) - 5490688 z^3 - 5490688 E^(4 Sqrt[z]) z^3 + 24150016 z^(7/2) - 24150016 E^(4 Sqrt[z]) z^(7/2) + 785408 z^4 + 785408 E^(4 Sqrt[z]) z^4 - 3190784 z^(9/2) + 3190784 E^(4 Sqrt[z]) z^(9/2) - 16384 z^5 - 16384 E^(4 Sqrt[z]) z^5 + 65536 z^(11/2) - 65536 E^(4 Sqrt[z]) z^(11/2) + 256 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (96577 - 12512 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 256 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (96577 - 12512 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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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'> -1 </cn> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3190784 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3190784 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 785408 </cn> <apply> <power /> <exponentiale /> <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]