Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0499)

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=-1/2

http://functions.wolfram.com/07.22.03.0499.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 6}, z] == (1/(2749862115 z^(9/2))) (8 (BesselI[1, 2 Sqrt[z]] (7780033800 + 4066835850 z - 461693925 z^2 + 65488500 z^3 + 104781600 z^4 + 113678208 z^5 + 671360256 z^6 - 148588488 z^7 + 7554912 z^8 - 118144 z^9 + 512 z^10 + 2 Pi z^(13/2) (352546425 - 75209904 z + 3792096 z^2 - 59136 z^3 + 256 z^4) StruveL[0, 2 Sqrt[z]]) - 2 Sqrt[z] BesselI[0, 2 Sqrt[z]] (3890016900 + 88409475 z + 49116375 z^2 - 65488500 z^3 - 62868960 z^4 - 152724096 z^5 + 741355776 z^6 - 152294040 z^7 + 7613664 z^8 - 118400 z^9 + 512 z^10 + Pi z^6 (352546425 - 75209904 z + 3792096 z^2 - 59136 z^3 + 256 z^4) StruveL[1, 2 Sqrt[z]])))

Standard Form

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MathML Form

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</ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 62868960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 65488500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 49116375 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 88409475 </cn> <ci> z </ci> </apply> <cn type='integer'> 3890016900 </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]