Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9b8)

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`=-9/2

http://functions.wolfram.com/07.22.03.a9b8.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(9/2), 19/4}, z] == (1/(824633720832 z^(15/4))) ((11 (4 z^(1/4) (1154218440375 + 1538957920500 Sqrt[z] + 925918484400 z + 296526484800 z^(3/2) + 47226816000 z^2 + 7841433600 z^(5/2) - 658022400 z^3 + 2480308224 z^(7/2) - 46989312 z^4 + 184811520 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (-1154218440375 + 1538957920500 Sqrt[z] - 925918484400 z + 296526484800 z^(3/2) - 47226816000 z^2 + 7841433600 z^(5/2) + 658022400 z^3 + 2480308224 z^(7/2) + 46989312 z^4 + 184811520 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1154218440375 + 305247852000 z - 60147360000 z^2 + 17108582400 z^3 + 9776332800 z^4 + 736100352 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-1154218440375 + 305247852000 z - 60147360000 z^2 + 17108582400 z^3 + 9776332800 z^4 + 736100352 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 305247852000 </cn> <ci> z </ci> </apply> <cn type='integer'> -1154218440375 </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 /> <cn type='integer'> -1 </cn> <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'> 16777216 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 736100352 </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]