Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8040)

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/07.22.03.8040.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 23/4}, z] == -(((2 Sqrt[z] (323328816698984971875 + 271646140979533320000 z - 10740829427808480000 z^2 + 2400613493870592000 z^3 - 1944140941364428800 z^4 - 618834968130355200 z^5 - 73165722007633920 z^6 - 5175575178117120 z^7 - 278455614701568 z^8 - 16767552323584 z^9 + 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]]^2 + (-969986450096954915625 - 2293013013562531260000 z - 165338341519871520000 z^2 - 1191671446597632000 z^3 + 2492280528224256000 z^4 + 675341227524096000 z^5 + 76891606808002560 z^6 + 5364983235870720 z^7 + 287088498966528 z^8 + 16080357556224 z^9 - 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (969986450096954915625 + 223708586689027440000 z + 3415935916384992000 z^2 - 1582252723408896000 z^3 + 2137803403051008000 z^4 + 639610941918412800 z^5 + 74578756852776960 z^6 + 5249714903580672 z^7 + 282218006052864 z^8 + 16492674416640 z^9 - 1099511627776 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (3390593641847193600 Sqrt[2] z^(17/4)))

Standard Form

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MathML Form

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</cn> <ci> z </ci> </apply> <cn type='integer'> 969986450096954915625 </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> <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'> 3390593641847193600 </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> </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]