Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aaj0)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aaj0.01

Input Form

HypergeometricPFQ[{-(5/4)}, {9/2, 11/4}, z] == -((1/(2568192 z^(7/2))) ((7 (4 (-2700 - 5400 Sqrt[z] + 1440 z + 10080 z^(3/2) - 945 z^2 + 14100 z^(5/2) + 4320 z^3 - 18048 z^(7/2) - 256 z^4 + 1024 z^(9/2) + E^(4 Sqrt[z]) (2700 - 5400 Sqrt[z] - 1440 z + 10080 z^(3/2) + 945 z^2 + 14100 z^(5/2) - 4320 z^3 - 18048 z^(7/2) + 256 z^4 + 1024 z^(9/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (47025 + 68400 z - 72960 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (47025 + 68400 z - 72960 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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<cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1440 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2700 </cn> </apply> </apply> <cn type='integer'> -2700 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]