Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8462)

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`=9/2

http://functions.wolfram.com/07.22.03.8462.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 13/4}, z] == (-4 (7502161379328000 + 15004322758656000 Sqrt[z] - 96027665655398400 z + 67877274447345825 z^(3/2) - 250928667511622100 z^2 + 134593410574854000 z^(5/2) - 779686945102296000 z^3 - 120039912231402240 z^(7/2) + 525578297196395520 z^4 + 17556702313328640 z^(9/2) - 72590075016560640 z^5 - 837558717972480 z^(11/2) + 3395766110650368 z^6 + 15559799341056 z^(13/2) - 62578332008448 z^7 - 113967628288 z^(15/2) + 456675819520 z^8 + 268435456 z^(17/2) - 1073741824 z^9 + E^(4 Sqrt[z]) (-7502161379328000 + 15004322758656000 Sqrt[z] + 96027665655398400 z + 67877274447345825 z^(3/2) + 250928667511622100 z^2 + 134593410574854000 z^(5/2) + 779686945102296000 z^3 - 120039912231402240 z^(7/2) - 525578297196395520 z^4 + 17556702313328640 z^(9/2) + 72590075016560640 z^5 - 837558717972480 z^(11/2) - 3395766110650368 z^6 + 15559799341056 z^(13/2) + 62578332008448 z^7 - 113967628288 z^(15/2) - 456675819520 z^8 + 268435456 z^(17/2) + 1073741824 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (279938369436350625 + 796269139730064000 z + 3430082448067968000 z^2 - 2152208594866176000 z^3 + 292817495900160000 z^4 - 13629323445534720 z^5 + 250654224285696 z^6 - 1827508584448 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (279938369436350625 + 796269139730064000 z + 3430082448067968000 z^2 - 2152208594866176000 z^3 + 292817495900160000 z^4 - 13629323445534720 z^5 + 250654224285696 z^6 - 1827508584448 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (13233854746932019200 z^(7/2))

Standard Form

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MathML Form

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type='integer'> 796269139730064000 </cn> <ci> z </ci> </apply> <cn type='integer'> 279938369436350625 </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> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 4 </cn> </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'> 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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]