Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1673)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=5

http://functions.wolfram.com/07.22.03.1673.01

Input Form

HypergeometricPFQ[{-(5/2)}, {5, 11/2}, z] == (1/(123002880 z^4)) (-4 (2 z (-161297325 - 148881600 z - 66724560 z^2 - 46041600 z^3 + 11647232 z^4 - 466944 z^5 + 4096 z^6) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (251648775 + 189466200 z + 81461520 z^2 + 40608000 z^3 - 11417344 z^4 + 464896 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]]) + Pi (-212837625 - 851350500 z - 681080400 z^2 - 302702400 z^3 - 172972800 z^4 + 46126080 z^5 - 1863680 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (212837625 + 851350500 z + 681080400 z^2 + 302702400 z^3 + 172972800 z^4 - 46126080 z^5 + 1863680 z^6 - 16384 z^7) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</apply> <apply> <times /> <cn type='integer'> 851350500 </cn> <ci> z </ci> </apply> <cn type='integer'> 212837625 </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 <sep /> 2 </cn> </apply> </apply> </apply> </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]