Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7993)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7993.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 23/4}, -z] == ((2 Sqrt[z] (-13256481484658383846875 + 11528981806866664140000 z + 156886541314382880000 z^2 + 63607622287233024000 z^3 + 45263381238241689600 z^4 - 11814370653870489600 z^5 + 1101211714914877440 z^6 - 57120735017041920 z^7 + 1957822187175936 z^8 - 49615462203392 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]]^2 + (39769444453975151540625 - 95188003636181175720000 z + 9419003091504246240000 z^2 + 24040676140056576000 z^3 - 55760127041912832000 z^4 + 12632866084513382400 z^5 - 1140949525431582720 z^6 + 58440503305175040 z^7 - 1990678686990336 z^8 + 50302656970752 z^9 - 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (39769444453975151540625 - 10346522134367519100000 z + 274648290844191264000 z^2 + 43111404808851456000 z^3 + 48815001144999936000 z^4 - 12116877610844160000 z^5 + 1116368502836428800 z^6 - 57631595607097344 z^7 + 1970655549456384 z^8 - 49890340110336 z^9 + 1099511627776 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(74593060120638259200 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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-1 </cn> <apply> <times /> <cn type='integer'> 10346522134367519100000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 39769444453975151540625 </cn> </apply> <apply> <power /> <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'> 74593060120638259200 </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]