Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7s0)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a7s0.01

Input Form

HypergeometricPFQ[{-(17/4)}, {5/2, -(1/4)}, z] == (1/(24227280 z^(3/2))) ((626535 - 626535 E^(4 Sqrt[z]) + 1253070 Sqrt[z] + 1253070 E^(4 Sqrt[z]) Sqrt[z] - 2864160 z + 2864160 E^(4 Sqrt[z]) z + 4714560 z^(3/2) + 4714560 E^(4 Sqrt[z]) z^(3/2) - 9665280 z^2 + 9665280 E^(4 Sqrt[z]) z^2 + 49125888 z^(5/2) + 49125888 E^(4 Sqrt[z]) z^(5/2) + 4369296 z^3 - 4369296 E^(4 Sqrt[z]) z^3 - 18324288 z^(7/2) - 18324288 E^(4 Sqrt[z]) z^(7/2) - 296448 z^4 + 296448 E^(4 Sqrt[z]) z^4 + 1198080 z^(9/2) + 1198080 E^(4 Sqrt[z]) z^(9/2) + 4096 z^5 - 4096 E^(4 Sqrt[z]) z^5 - 16384 z^(11/2) - 16384 E^(4 Sqrt[z]) z^(11/2) - 4 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-13037895 + 4635696 z - 300288 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 4 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-13037895 + 4635696 z - 300288 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 4 </cn> <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'> 4096 </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'> 300288 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4635696 </cn> <ci> z </ci> </apply> <cn type='integer'> -13037895 </cn> </apply> <apply> <ci> Erfi </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> 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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]