Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8520)

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`=11/2

http://functions.wolfram.com/07.22.03.8520.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 23/4}, z] == ((2 Sqrt[z] (13256481484658383846875 + 32804848890400466880000 z + 25030689981473528352000 z^2 + 13550761986512073523200 z^3 + 24833523381755874508800 z^4 - 6686839281798453657600 z^5 + 467251365625599098880 z^6 - 12469857165005291520 z^7 + 142113110545661952 z^8 - 680597697593344 z^9 + 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]]^2 - (39769444453975151540625 + 63506765268124198020000 z + 40343991894015761952000 z^2 + 21746231936777495347200 z^3 + 21313990517017205145600 z^4 - 6414201863566943846400 z^5 + 459688664545194147840 z^6 - 12382166871409950720 z^7 + 141689583820603392 z^8 - 679910502825984 z^9 + 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (31862185260018637899375 + 45894132135630186408000 z + 31469586134712082156800 z^2 + 17815867548446357913600 z^3 + 23323813673846095872000 z^4 - 6574648198791639859200 z^5 + 464188181906813091840 z^6 - 12434592721841160192 z^7 + 141943390617993216 z^8 - 680322819686400 z^9 + 1099511627776 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(28104365123894771712000 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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31862185260018637899375 </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'> 28104365123894771712000 </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]