Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9083)

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/07.22.03.9083.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 9/4}, -z] == ((4 z (-5334008855175 - 5418675662400 z + 907273509347205 z^2 + 1211500820930400 z^3 + 300581862577920 z^4 + 21940424884224 z^5 + 574513938432 z^6 + 5593104384 z^7 + 16777216 z^8) BesselJ[1/4, Sqrt[z]]^2 - 6 Sqrt[z] (-17780029517250 - 16481805139800 z + 181229662689075 z^2 + 977501483038080 z^3 + 282196855100160 z^4 + 21445873827840 z^5 + 569644744704 z^6 + 5578424320 z^7 + 16777216 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-133350221379375 - 111760185537000 z - 173397621196800 z^2 + 960972603891300 z^3 + 4024233830897280 z^4 + 1138702498053120 z^5 + 86059978260480 z^6 + 2281342500864 z^7 + 22322085888 z^8 + 67108864 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (1583283904282080 Sqrt[2] z^(13/4))

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]