Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0445)

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=-5/2

http://functions.wolfram.com/07.22.03.0445.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(5/2), 6}, z] == (1/(13749310575 z^(9/2))) (8 (BesselI[1, 2 Sqrt[z]] (505702197000 + 328706428050 z - 7455865725 z^2 + 1807482600 z^3 + 261954000 z^4 + 37497600 z^5 + 8402688 z^6 + 4552704 z^7 + 19992576 z^8 - 944128 z^9 + 8192 z^10 + 512 Pi z^(17/2) (39501 - 1848 z + 16 z^2) StruveL[0, 2 Sqrt[z]]) - 2 Sqrt[z] BesselI[0, 2 Sqrt[z]] (252851098500 + 37927664775 z - 1620840375 z^2 - 392931000 z^3 - 52390800 z^4 - 9192960 z^5 - 3177216 z^6 - 4884480 z^7 + 20459520 z^8 - 948224 z^9 + 8192 z^10 + 256 Pi z^8 (39501 - 1848 z + 16 z^2) StruveL[1, 2 Sqrt[z]])))

Standard Form

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MathML Form

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<power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4552704 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8402688 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 37497600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 261954000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1807482600 </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'> 7455865725 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 328706428050 </cn> <ci> z </ci> </apply> <cn 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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]