Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a94a)

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

For fixed z and a₁=-11/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a94a.01

Input Form

HypergeometricPFQ[{-(11/4)}, {5/2, 9/4}, z] == (1/(130351104 z^(3/2))) ((4 (709632 - 878031 Sqrt[z] + 6398700 z + 1469232 z^(3/2) - 6397632 z^2 - 187648 z^(5/2) + 762880 z^3 + 4096 z^(7/2) - 16384 z^4 + E^(4 Sqrt[z]) (-709632 - 878031 Sqrt[z] - 6398700 z + 1469232 z^(3/2) + 6397632 z^2 - 187648 z^(5/2) - 762880 z^3 + 4096 z^(7/2) + 16384 z^4)) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (-2297295 - 29405376 z + 26138112 z^2 - 3063808 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (-2297295 - 29405376 z + 26138112 z^2 - 3063808 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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<cn type='integer'> 29405376 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -2297295 </cn> </apply> <apply> <ci> Erfi </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> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]