Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8181)

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/07.22.03.8181.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 19/4}, -z] == ((2 Sqrt[z] (-14244766981570125 + 6906553688034000 z + 1804160963404800 z^2 + 9768609497088000 z^3 - 10210656160972800 z^4 + 8170680782684160 z^5 + 6578067556270080 z^6 + 556032908591104 z^7 + 12210592022528 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - (-42734300944710375 + 85838595836994000 z + 19845770597452800 z^2 + 5921348802969600 z^3 - 9066473275392000 z^4 + 4862027476500480 z^5 + 6250257532846080 z^6 + 548516715823104 z^7 + 12167642349568 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (42734300944710375 + 5327912845054800 z + 5412482890214400 z^2 + 10362360405196800 z^3 - 10502345126707200 z^4 + 6722167788011520 z^5 + 6443702591422464 z^6 + 553007104131072 z^7 + 12193412153344 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(22254374721945600 Sqrt[2] z^(13/4))

Standard Form

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MathML Form

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<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'> 22254374721945600 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <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]