Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8999)

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`=7/2

http://functions.wolfram.com/07.22.03.8999.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 21/4}, -z] == ((2 Sqrt[z] (92905480235643075 + 444675802837266000 z - 2439364404135859200 z^2 + 15153459727477800960 z^3 + 15225960306870190080 z^4 + 2725874301010968576 z^5 + 153415812718264320 z^6 + 3255924512784384 z^7 + 26607322398720 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (154842467059405125 + 851236536859909200 z - 3704220021095193600 z^2 + 5049044016810393600 z^3 + 13047827745427292160 z^4 + 2596273642788618240 z^5 + 150605715877134336 z^6 + 3232744574287872 z^7 + 26547192856576 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (464527401178215375 + 1562717821399534800 z - 4356107425250380800 z^2 + 6023661752741068800 z^3 + 13323372869916426240 z^4 + 2613938938026393600 z^5 + 150999853751599104 z^6 + 3236036666720256 z^7 + 26555782791168 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (11665560858399866880 Sqrt[2] z^(15/4))

Standard Form

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MathML Form

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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]