Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8429)

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`=9/2

http://functions.wolfram.com/07.22.03.8429.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(21/4)}, -z] == ((4 z (111946779382370625 + 15352701172439400 z + 12894115638096000 z^2 - 4629607604582400 z^3 + 565561219645440 z^4 - 37752676024320 z^5 + 1669140054016 z^6 - 56774098944 z^7 + 2147483648 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (335840338147111875 - 17911484701179300 z + 8935910974267200 z^2 - 2541071927116800 z^3 + 296477980508160 z^4 - 19458116812800 z^5 + 854115483648 z^6 - 29058138112 z^7 + 1073741824 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (1007521014441335625 - 245643218759030400 z + 27073580562151200 z^2 + 57644153369510400 z^3 - 19162334680473600 z^4 + 2303183760261120 z^5 - 152784366206976 z^6 + 6736689758208 z^7 - 229243879424 z^8 + 8589934592 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(23533824466152000 Sqrt[2] z^(11/4))

Standard Form

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MathML Form

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<times /> <cn type='integer'> 23533824466152000 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <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]