Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ai)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8ai.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, -(7/4)}, z] == (1/(7752326400 z^(7/2))) ((10854718875 - 10854718875 E^(4 Sqrt[z]) + 21709437750 Sqrt[z] + 21709437750 E^(4 Sqrt[z]) Sqrt[z] + 15713497800 z - 15713497800 E^(4 Sqrt[z]) z + 2481078600 z^(3/2) + 2481078600 E^(4 Sqrt[z]) z^(3/2) - 1816214400 z^2 + 1816214400 E^(4 Sqrt[z]) z^2 + 778377600 z^(5/2) + 778377600 E^(4 Sqrt[z]) z^(5/2) - 319334400 z^3 + 319334400 E^(4 Sqrt[z]) z^3 + 141281280 z^(7/2) + 141281280 E^(4 Sqrt[z]) z^(7/2) - 72253440 z^4 + 72253440 E^(4 Sqrt[z]) z^4 + 45711360 z^(9/2) + 45711360 E^(4 Sqrt[z]) z^(9/2) - 39321600 z^5 + 39321600 E^(4 Sqrt[z]) z^5 + 55050240 z^(11/2) + 55050240 E^(4 Sqrt[z]) z^(11/2) - 226492416 z^6 + 226492416 E^(4 Sqrt[z]) z^6 - 2097152 z^(13/2) - 2097152 E^(4 Sqrt[z]) z^(13/2) + 8388608 z^7 - 8388608 E^(4 Sqrt[z]) z^7 + 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (-435 + 16 z) Erf[Sqrt[2] z^(1/4)] + 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (-435 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 39321600 </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='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 39321600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45711360 </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'> 45711360 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> 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type='integer'> 319334400 </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='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 319334400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 778377600 </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'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 778377600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1816214400 </cn> <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]