Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8376)

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`=5/2

http://functions.wolfram.com/07.22.03.8376.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 23/4}, z] == ((2 Sqrt[z] (-11916295455736546875 + 1210544300265300000 z - 6514929325064160000 z^2 + 112690669406515200000 z^3 + 1031251829752243814400 z^4 - 625665185696710656000 z^5 + 83539421171181158400 z^6 - 3796247300737597440 z^7 + 67942538626990080 z^8 - 481448654012416 z^9 + 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]]^2 + (35748886367209640625 + 50842860611142600000 z - 24475004761727520000 z^2 - 270457606575636480000 z^3 - 745444825813558886400 z^4 + 579110540754183782400 z^5 - 81275459634148147200 z^6 + 3754579106432286720 z^7 - 67643480054169600 z^8 + 480761459245056 z^9 - 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (35748886367209640625 - 25421430305571300000 z + 41378605172704800000 z^2 + 227566202649233817600 z^3 + 901597688591420620800 z^4 - 606146782176372326400 z^5 + 82616033636410982400 z^6 - 3779447707957985280 z^7 + 67822605960216576 z^8 - 481173776105472 z^9 + 1099511627776 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1414734026731683840000 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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25421430305571300000 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 35748886367209640625 </cn> </apply> <apply> <power /> <apply> <ci> BesselI </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> <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'> 1414734026731683840000 </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]