Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9094)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9094.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 21/4}, z] == ((2 Sqrt[z] (42271993507217599125 + 80094822664221565200 z + 57636039904053811200 z^2 + 97982791768634572800 z^3 - 70171919408244326400 z^4 + 8424137409869905920 z^5 - 336021123646881792 z^6 + 5303357971365888 z^7 - 33462090203136 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]]^2 - 3 (70453322512029331875 + 114755392376114490000 z + 77113081836203212800 z^2 + 47155272636074803200 z^3 - 63264512217386188800 z^4 + 8137735353925632000 z^5 - 331429644022579200 z^6 + 5274180111040512 z^7 - 33401960660992 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (93744361078298555625 + 123078261446534394000 z + 81087779174885683200 z^2 + 52748981273460326400 z^3 - 64169379794593382400 z^4 + 8177242841284608000 z^5 - 332076337248337920 z^6 + 5278329049448448 z^7 - 33410550595584 z^8 + 68719476736 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (63188454649665945600 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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<cn type='rational'> 5 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 5 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 63188454649665945600 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]