Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9145)

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`=-11/2

http://functions.wolfram.com/07.22.03.9145.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 23/4}, -z] == -(((2 Sqrt[z] (192122920067512809375 - 172085012724815190000 z + 1571953178315520000 z^2 - 584321989515264000 z^3 - 378474084030873600 z^4 + 81817083681177600 z^5 - 6093555986595840 z^6 + 236980189265920 z^7 - 5415953760256 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 + (-576368760202538428125 + 1394531244197361270000 z - 170893766956872960000 z^2 + 76215911675904000 z^3 + 443683079110656000 z^4 - 86097341133619200 z^5 + 6251565149061120 z^6 - 240480587612160 z^7 + 5458903433216 z^8 - 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-576368760202538428125 + 164944555765279290000 z - 6377638609165824000 z^2 - 439707182745600000 z^3 - 401868496060416000 z^4 + 83444293907251200 z^5 - 6155043141058560 z^6 + 238361021251584 z^7 - 5433133629440 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (592008413655859200 Sqrt[2] z^(17/4)))

Standard Form

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MathML Form

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</cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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]