Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8222)

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`=-1/2

http://functions.wolfram.com/07.22.03.8222.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 13/4}, z] == (4 z^(1/4) (-17392877877375 - 23190503836500 Sqrt[z] + 21925567263600 z + 43369253928000 z^(3/2) + 13635165922560 z^2 + 189182213176320 z^(5/2) + 169620473917440 z^3 - 790675083018240 z^(7/2) - 45375855329280 z^4 + 189353871802368 z^(9/2) + 2787304800256 z^5 - 11303133380608 z^(11/2) - 52227473408 z^6 + 209715200000 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-17392877877375 + 23190503836500 Sqrt[z] + 21925567263600 z - 43369253928000 z^(3/2) + 13635165922560 z^2 - 189182213176320 z^(5/2) + 169620473917440 z^3 + 790675083018240 z^(7/2) - 45375855329280 z^4 - 189353871802368 z^(9/2) + 2787304800256 z^5 + 11303133380608 z^(11/2) - 52227473408 z^6 - 209715200000 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-17392877877375 + 40477970332800 z - 323823762662400 z^2 - 1151373378355200 z^3 + 3289638223872000 z^4 - 765588532101120 z^5 + 45368209309696 z^6 - 839666106368 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-17392877877375 + 40477970332800 z - 323823762662400 z^2 - 1151373378355200 z^3 + 3289638223872000 z^4 - 765588532101120 z^5 + 45368209309696 z^6 - 839666106368 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(2391953186488320 z^(9/4))

Standard Form

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MathML Form

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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'> 839666106368 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45368209309696 </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'> 765588532101120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3289638223872000 </cn> <apply> <power /> <ci> 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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]