Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8a5)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8a5.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, -(21/4)}, -z] == ((4 z (85390373289375 + 3903559921800 z + 3979610611200 z^2 - 934162022400 z^3 + 68234772480 z^4 - 2275409920 z^5 + 33554432 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (256171119868125 - 37083819257100 z + 2354891616000 z^2 - 490510540800 z^3 + 34856632320 z^4 - 1148190720 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (768513359604375 - 257634954838800 z + 20651091199200 z^2 + 16978477824000 z^3 - 3808685260800 z^4 + 275266928640 z^5 - 9135194112 z^6 + 134217728 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (6424740504000 Sqrt[2] z^(11/4))

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]