Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9r2)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a9r2.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(9/2), 13/4}, z] == (1/(402653184 z^(9/4))) ((-4 z^(1/4) (204417675 + 272556900 Sqrt[z] + 121136400 z - 4614720 z^(3/2) + 2797824 z^2 - 4764672 z^(5/2) + 45056 z^3 - 180224 z^(7/2) + E^(4 Sqrt[z]) (204417675 - 272556900 Sqrt[z] + 121136400 z + 4614720 z^(3/2) + 2797824 z^2 + 4764672 z^(5/2) + 45056 z^3 + 180224 z^(7/2))) + 11 E^(2 Sqrt[z]) Sqrt[2 Pi] (18583425 - 8809920 z + 9192960 z^2 + 1720320 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + 11 E^(2 Sqrt[z]) Sqrt[2 Pi] (18583425 - 8809920 z + 9192960 z^2 + 1720320 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<times /> <cn type='integer'> -180224 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 45056 </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'> 4764672 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2797824 </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'> 4614720 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 121136400 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 272556900 </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]