Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8855)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.8855.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 21/4}, -z] == ((2 Sqrt[z] (-5574039253657875 - 9299593694991600 z - 5321973142886400 z^2 + 67670650865664000 z^3 + 258968630830694400 z^4 + 173467367406305280 z^5 + 25357155934666752 z^6 + 1113381150916608 z^7 + 16325170692096 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (-9290065422763125 - 22105591570062000 z - 9954060878361600 z^2 - 9461285587353600 z^3 + 138404910809088000 z^4 + 152821805875200000 z^5 + 24406602295541760 z^6 + 1099198095163392 z^7 + 16265041149952 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, 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[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (72716601891225600 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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</apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 72716601891225600 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <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]