Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0934)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=5/2

http://functions.wolfram.com/07.22.03.0934.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5/2, 4}, -z] == (1/(5189184000 z^(5/2))) (4 (2 Sqrt[z] (-10886400 - 76204800 z + 1006439175 z^2 + 1146575700 z^3 + 219126240 z^4 + 11845248 z^5 + 207616 z^6 + 1024 z^7) BesselJ[0, 2 Sqrt[z]] - (-21772800 - 141523200 z + 580763925 z^2 + 1046488500 z^3 + 213380640 z^4 + 11742336 z^5 + 207104 z^6 + 1024 z^7) BesselJ[1, 2 Sqrt[z]]) + Pi z^(3/2) (-638512875 + 3064861800 z + 4378374000 z^2 + 864864000 z^3 + 47174400 z^4 + 829440 z^5 + 4096 z^6) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(3/2) (-638512875 + 3064861800 z + 4378374000 z^2 + 864864000 z^3 + 47174400 z^4 + 829440 z^5 + 4096 z^6) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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<times /> <cn type='integer'> 580763925 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 141523200 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -21772800 </cn> </apply> <apply> <ci> BesselJ </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> </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]