Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7858)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-3/4

http://functions.wolfram.com/07.22.03.7858.01

Input Form

HypergeometricPFQ[{6}, {-(3/4), 23/4}, z] == -((1/(268435456 z^(19/4))) ((1463 (16 E^(2 Sqrt[z]) z^(3/4) (12006225 + 4158000 z + 710640 z^2 + 87552 z^3 + 4096 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (36018675 - 72037350 Sqrt[z] + 74220300 z - 52390800 z^(3/2) + 28576800 z^2 - 12912480 z^(5/2) + 5088960 z^3 - 1831680 z^(7/2) + 645120 z^4 - 245760 z^(9/2) + 49152 z^5 + 65536 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (-36018675 - 72037350 Sqrt[z] - 74220300 z - 52390800 z^(3/2) - 28576800 z^2 - 12912480 z^(5/2) - 5088960 z^3 - 1831680 z^(7/2) - 645120 z^4 - 245760 z^(9/2) - 49152 z^5 + 65536 z^(11/2)) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

Standard Form

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MathML Form

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<times /> <cn type='integer'> 52390800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 74220300 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 72037350 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -36018675 </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> </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]