Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0581)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=2

http://functions.wolfram.com/07.22.03.0581.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 11/2}, z] == (1/(136031345049600 z^4)) (4 (2 z (737482370625 - 646175029500 z + 809123515200 z^2 + 25425205344000 z^3 - 31810051146240 z^4 + 6820431206400 z^5 - 440974295040 z^6 + 10461052928 z^7 - 93782016 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (2212447111875 - 1545201157500 z + 2067760094400 z^2 + 13937150304000 z^3 - 28742798292480 z^4 + 6608685864960 z^5 - 435824640000 z^6 + 10414391296 z^7 - 93650944 z^8 + 262144 z^9) BesselI[1, 2 Sqrt[z]]) + Pi (2212447111875 - 2528510985000 z + 3034213182000 z^2 - 10788313536000 z^3 - 75518194752000 z^4 + 120829111603200 z^5 - 26850913689600 z^6 + 1753529057280 z^7 - 41750691840 z^8 + 374865920 z^9 - 1048576 z^10) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (-2212447111875 + 2528510985000 z - 3034213182000 z^2 + 10788313536000 z^3 + 75518194752000 z^4 - 120829111603200 z^5 + 26850913689600 z^6 - 1753529057280 z^7 + 41750691840 z^8 - 374865920 z^9 + 1048576 z^10) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 75518194752000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10788313536000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3034213182000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2528510985000 </cn> <ci> z </ci> </apply> <cn type='integer'> -2212447111875 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveL </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 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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]