Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7386)

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, b₁>=-23/4

For fixed z and a₁=5, b₁=-23/4

http://functions.wolfram.com/07.22.03.7386.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), 19/4}, z] == (1/(343670784 z^(15/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (-50414138775 - 16816199400 z - 2704862160 z^2 - 281529984 z^3 - 9373440 z^4 + 1308672 z^5 + 32768 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-151242416325 + 302484832650 Sqrt[z] - 309721311900 z + 216129513600 z^(3/2) - 115848532800 z^2 + 51074543520 z^(5/2) - 19468088640 z^3 + 6711344640 z^(7/2) - 2110268160 z^4 + 545825280 z^(9/2) - 80231424 z^5 - 10862592 z^(11/2) + 9797632 z^6 - 2490368 z^(13/2) + 262144 z^7) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (151242416325 + 302484832650 Sqrt[z] + 309721311900 z + 216129513600 z^(3/2) + 115848532800 z^2 + 51074543520 z^(5/2) + 19468088640 z^3 + 6711344640 z^(7/2) + 2110268160 z^4 + 545825280 z^(9/2) + 80231424 z^5 - 10862592 z^(11/2) - 9797632 z^6 - 2490368 z^(13/2) - 262144 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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115848532800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 216129513600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 309721311900 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 302484832650 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 151242416325 </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> </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]