Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8185)

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`=-3/2

http://functions.wolfram.com/07.22.03.8185.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 23/4}, -z] == ((2 Sqrt[z] (-5341787618088796875 + 3711779282054844000 z + 615669928761888000 z^2 + 134710685267558400 z^3 + 360771140704665600 z^4 - 311020985253888000 z^5 + 208263577054740480 z^6 + 147131502805647360 z^7 + 10985912162844672 z^8 + 215916595904512 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]]^2 - (-16025362854266390625 + 35554938385999032000 z + 2131165138021920000 z^2 + 808264111605350400 z^3 + 290146091345510400 z^4 - 291921720665702400 z^5 + 132419094514237440 z^6 + 140615189161574400 z^7 + 10852811126341632 z^8 + 215229401137152 z^9 + 1099511627776 z^10) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (16025362854266390625 - 1367497630230732000 z + 161021365983878400 z^2 + 217609568509132800 z^3 + 392550594173337600 z^4 - 322174009737216000 z^5 + 175395106361180160 z^6 + 144467343181873152 z^7 + 10932362510598144 z^8 + 215641717997568 z^9 + 1099511627776 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(787102095428812800 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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<cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 787102095428812800 </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]