Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8366)

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`=5/2

http://functions.wolfram.com/07.22.03.8366.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 13/4}, z] == (-4 z^(1/4) (1146348769190625 - 9141275602790100 Sqrt[z] + 9229819254994800 z - 69918472082289600 z^(3/2) - 20418950270073600 z^2 + 93890681903692800 z^(5/2) + 5039083672842240 z^3 - 21143421084549120 z^(7/2) - 357868102287360 z^4 + 1458236184330240 z^(9/2) + 9219085434880 z^5 - 37141388197888 z^(11/2) - 89271566336 z^6 + 357891571712 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (1146348769190625 + 9141275602790100 Sqrt[z] + 9229819254994800 z + 69918472082289600 z^(3/2) - 20418950270073600 z^2 - 93890681903692800 z^(5/2) + 5039083672842240 z^3 + 21143421084549120 z^(7/2) - 357868102287360 z^4 - 1458236184330240 z^(9/2) + 9219085434880 z^5 + 37141388197888 z^(11/2) - 89271566336 z^6 - 357891571712 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (1146348769190625 + 29346528491280000 z + 328681119102336000 z^2 - 389547993010176000 z^3 + 85614943518720000 z^4 - 5860274208768000 z^5 + 148832360857600 z^6 - 1432371593216 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (1146348769190625 + 29346528491280000 z + 328681119102336000 z^2 - 389547993010176000 z^3 + 85614943518720000 z^4 - 5860274208768000 z^5 + 148832360857600 z^6 - 1432371593216 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(1517395302678528000 z^(9/4))

Standard Form

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MathML Form

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type='integer'> 89271566336 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 37141388197888 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9219085434880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1458236184330240 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 357868102287360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21143421084549120 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5039083672842240 </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'> 93890681903692800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20418950270073600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 69918472082289600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9229819254994800 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 9141275602790100 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1146348769190625 </cn> </apply> </apply> <cn type='integer'> 1146348769190625 </cn> </apply> 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</apply> <apply> <times /> <cn type='integer'> 85614943518720000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 389547993010176000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 328681119102336000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 29346528491280000 </cn> <ci> z </ci> </apply> <cn type='integer'> 1146348769190625 </cn> </apply> <apply> <ci> Erf </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> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4294967296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1432371593216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 148832360857600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5860274208768000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 85614943518720000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </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]