Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9481)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.9481.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, 23/4}, -z] == ((2 Sqrt[z] (9290065422763125 - 3375730732374000 z - 985550582016000 z^2 + 1576880931225600 z^3 + 183226758414336000 z^4 + 161296911433728000 z^5 + 24808058592952320 z^6 + 1105250777825280 z^7 + 16290810953728 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - (27870196268289375 - 52596062701182000 z - 17528721065856000 z^2 - 6307523724902400 z^3 + 113535427048243200 z^4 + 147469561705267200 z^5 + 24143840893992960 z^6 + 1095184448225280 z^7 + 16247861280768 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-27870196268289375 - 6860356004502000 z - 6166730784614400 z^2 - 11038166518579200 z^3 + 150839652689510400 z^4 + 155497927960166400 z^5 + 24537982996316160 z^6 + 1101204918632448 z^7 + 16273631084544 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (278765325464371200 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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<apply> <ci> BesselJ </ci> <cn type='rational'> 3 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 278765325464371200 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]