Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7387)

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/07.22.03.7387.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), 19/4}, -z] == (1/(85917696 z^(15/4))) (-4 z^(3/4) (-50414138775 + 16816199400 z - 2704862160 z^2 + 281529984 z^3 - 9373440 z^4 - 1308672 z^5 + 32768 z^6) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((151242416325 - 309721311900 z + 115848532800 z^2 - 19468088640 z^3 + 2110268160 z^4 - 80231424 z^5 - 9797632 z^6 + 262144 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[z] (151242416325 - 108064756800 z + 25537271760 z^2 - 3355672320 z^3 + 272912640 z^4 + 5431296 z^5 - 1245184 z^6) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-151242416325 + 108064756800 z - 25537271760 z^2 + 3355672320 z^3 - 272912640 z^4 - 5431296 z^5 + 1245184 z^6) Cos[2 Sqrt[z]] + (151242416325 - 309721311900 z + 115848532800 z^2 - 19468088640 z^3 + 2110268160 z^4 - 80231424 z^5 - 9797632 z^6 + 262144 z^7) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9797632 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 80231424 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2110268160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 19468088640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 115848532800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 309721311900 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 151242416325 </cn> 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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]