Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1674)

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/07.22.03.1674.01

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) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (-251648775 + 189466200 z - 81461520 z^2 + 40608000 z^3 + 11417344 z^4 + 464896 z^5 + 4096 z^6) BesselJ[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) BesselJ[1, 2 Sqrt[z]] StruveH[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) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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<ci> BesselJ </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> StruveH </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> </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]