Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0647)

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=5

http://functions.wolfram.com/07.22.03.0647.01

Input Form

HypergeometricPFQ[{-(11/2)}, {5, 11/2}, z] == (4 (2 z (688833730864125 + 995902283722500 z + 715659375816000 z^2 + 979538912352000 z^3 - 476055772531200 z^4 + 47339234334720 z^5 - 1656188682240 z^6 + 23610195968 z^7 - 137035776 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (1139460656016375 + 1367097912526500 z + 938756167272000 z^2 + 776501709984000 z^3 - 453735048844800 z^4 + 46531191306240 z^5 - 1644502302720 z^6 + 23541907456 z^7 - 136904704 z^8 + 262144 z^9) BesselI[1, 2 Sqrt[z]]) - Pi (714620417135625 + 4083545240775000 z + 4900254288930000 z^2 + 3484625272128000 z^3 + 3484625272128000 z^4 - 1858466811801600 z^5 + 187723920384000 z^6 - 6601280716800 z^7 + 94304010240 z^8 - 547880960 z^9 + 1048576 z^10) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (714620417135625 + 4083545240775000 z + 4900254288930000 z^2 + 3484625272128000 z^3 + 3484625272128000 z^4 - 1858466811801600 z^5 + 187723920384000 z^6 - 6601280716800 z^7 + 94304010240 z^8 - 547880960 z^9 + 1048576 z^10) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])/(3432665972736000 z^4)

Standard Form

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MathML Form

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type='integer'> 3484625272128000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3484625272128000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4900254288930000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4083545240775000 </cn> <ci> z </ci> </apply> <cn type='integer'> 714620417135625 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </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'> 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> </apply> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> 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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]