Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad9w)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ad9w.01

Input Form

HypergeometricPFQ[{9/4}, {-(11/2), 21/4}, z] == (221 (4 z^(1/4) (-1012042268362125 - 1349389691149500 Sqrt[z] - 1015635317835600 z - 531695278699200 z^(3/2) - 207649109606400 z^2 - 62923972608000 z^(5/2) - 15101753425920 z^3 - 2876524462080 z^(7/2) - 427378606080 z^4 - 47311749120 z^(9/2) - 3523215360 z^5 - 134217728 z^(11/2) + E^(4 Sqrt[z]) (-1012042268362125 + 1349389691149500 Sqrt[z] - 1015635317835600 z + 531695278699200 z^(3/2) - 207649109606400 z^2 + 62923972608000 z^(5/2) - 15101753425920 z^3 + 2876524462080 z^(7/2) - 427378606080 z^4 + 47311749120 z^(9/2) - 3523215360 z^5 + 134217728 z^(11/2))) + 6336947925 E^(2 Sqrt[z]) Sqrt[2 Pi] (159705 - 10080 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 6336947925 E^(2 Sqrt[z]) Sqrt[2 Pi] (159705 - 10080 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(1240171806720 z^(17/4))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 256 </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'> 10080 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 159705 </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> </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]