Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8r8)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8r8.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 19/4}, z] == (-4 z^(1/4) (271993769775 + 4227185207700 Sqrt[z] - 529293229920 z + 4402593336960 z^(3/2) - 292943589120 z^2 + 3108566522880 z^(5/2) + 904742092800 z^3 - 3887181398016 z^(7/2) - 97641234432 z^4 + 398073790464 z^(9/2) + 2560622592 z^5 - 10292822016 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-271993769775 + 4227185207700 Sqrt[z] + 529293229920 z + 4402593336960 z^(3/2) + 292943589120 z^2 + 3108566522880 z^(5/2) - 904742092800 z^3 - 3887181398016 z^(7/2) + 97641234432 z^4 + 398073790464 z^(9/2) - 2560622592 z^5 - 10292822016 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (5524796502225 + 18750824492400 z + 18368154604800 z^2 + 14842953216000 z^3 - 15832483430400 z^4 + 1599914115072 z^5 - 41221619712 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (5524796502225 + 18750824492400 z + 18368154604800 z^2 + 14842953216000 z^3 - 15832483430400 z^4 + 1599914115072 z^5 - 41221619712 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(76014478688256 z^(15/4))

Standard Form

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MathML Form

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<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> <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'> 268435456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 41221619712 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1599914115072 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </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]